Eatchel - The Cub

If you don't have her yet but want to try her out, Eatchel is available as a Trial Operative in Story Chapter 12B "Skyward Blaze" (Legacy // Yehrus // Skyward Blaze)
Due to her being the games best healer, Eatchel is also commonly available as a support operative in the operative/outfit trials of other operatives.

Eatchel is Snowbreak's best healer - no other operative even comes close to Eatchel in terms of healing.
With her 5* weapon Eatchel can passively grant your other operatives a sizable ATK boost, and her M1 also gives your other operatives a good ATK boost as well, but beyond her logistics Special Talent that's as much as you really need to invest into her - she's not good as a main DPS, having both poor dps and little AoE.
Whilst Eatchel is MVP for casual play due to her completely passive healing, and is an incredible versatile support that works well with almost all dps operatives, at endgame her buffs aren't strong enough to make her an optimal support for anybody other than Clarina - Crimson Moon, as healers just aren't needed at endgame.

Overall

Role: Support: Healer and ATK buffer
Deals Kinetic Damage
(Although ideally doesn't deal damage)
Weapon Type: Shotgun
Deals mostly ballistic damage
Mobility is good

How to use Eatchel - The Cub

Add Eatchel to your team and keep her off-field.

That's it.

Do not use Eatchel's Support Skill.

How to build Eatchel - The Cub

Weapon: Blitzing Fangs
Weapon Parts: Max ATK
Logistics Squad: Lux
Basic Stats: +10.0% ATK
+106 Alignment Index
Special Stat: +10.6% Healing Bonus
Best teammates:
Eatchel is a good support for all operatives.
Works extra well with Clarina - Crimson Moon

Specifics:

Standard Skill

Eatchel lunges forward, pulling enemies together in front of her, dealing Kinetic DMG, and recovering some HP.
Her next 2 shots deal AoE damage, have a higher fire rate, and recover more U-Energy.

Whilst her standard skill is good for clearing a group of trash mobs, Eatchel is generally not a good main DPS - if she fails to group up enemies or her 2 special shots fail to kill enemies she just has to run around shooting things with her gun, which is completely unbuffed, which is about the least effective way of playing possible.
Her standard skill also doesn't really help her against bosses at all, against which she performs very poorly.

Ultimate Skill

Eatchel's Ultimate Skill deals AoE Kinetic DMG in front of her.
This also restores HP to your entire team.

Using her ult also causes Eatchel to gain Icebound Claws.
Icebound Claws are charged by her ult dealing damage.
Maxing her Icebound Claws does not require much investment.

These Icebound Claws automatically restore HP to operatives who drop below 30% HP.
Icebound Claws also provide the squad with a passive ATK buff.
The most charged Icebound Claw is automatically lost every 20s.

With M1 and a Kinetic Weapon equipped, Eatchel always has 2 Icebound Claws.
If she has 2 or fewer Icebound Claws they no longer disappear every 20s.
This means M1 gives Eatchel an extra passive ATK boost that never disappears.
For a passively healing Eatchel who isn't getting any ATK buffs from other operatives, this is generally around a +100-110 ATK buff per Claw.

The number of Icebound Claws Eatchel has can be viewed as the small gauge to the right of your HP bar and S-Energy gauge.
(See the image to the right.)

Eatchel's Icebound Claws

Support Skill

Whilst her support skill is off-cooldown: Eatchel passive heals your current operative.
This is a very strong heal - getting over 500HP/s is not overly difficult.

Actually using her Support Skill causes Eatchel to leap towards the target and deal Kinetic DMG, whilst also doing a little healing.
This healing is 12x the healing she does each second whilst this skill is off-cooldown.
This skill also has a 12s cooldown, however it only goes on cooldown after Eatchel returns from her pounce, which takes 1.1 seconds.
As such, using her support skill does slightly reduced healing compared to her passive healing, although the difference is relatively minor.

Eatchel's support skill can be actively used in order to proc the buffs from certain 4* weapons.
Once Eatchel has her signature 5* weapon (Blitzing Fangs) there is no reason to ever actively use her support skill - Once she has that 5* weapon, the passive healing Eatchel provides from her support skill being off-cooldown is both the strongest heal she can provide, but is also the strongest ATK boost she can provide as well.

Again: Once Eatchel has Blitzing Fangs, there is literally no reason to ever use her support skill, and using her support skill results in a significant reduction in Eatchel's effectiveness - both for her healing but also for the buffs she provides to her team.

Weapon

Blitzing Fangs
Eatchel's 5* weapon, and her best weapon by a significant margin.
This gives Eatchel more healing (very good), as well as giving another strong ATK bonus to the squad, which is excellent.
It also gives Eatchel another passive healing effect, which is great.
Blitzing Fangs provides more healing than any other weapon Eatchel can equip, provides more ATK buffs, and can do so entirely passively with 100% guaranteed uptime.

Blitzing Fangs is the only weapon Eatchel can use that actually buffs her passive healing.
As such, if you don't have Blitzing Fangs and are using Eatchel's passive healing (i.e. not actively using her support skill) then it doesn't matter which weapon Eatchel uses, as no non-5* weapon buffs her passive healing.

If you don't have Blitzing Fangs and are ok with spamming Eatchel's support skill off-cooldown:

Lapis Lazuli provides a decent ATK boost to the deployed operative after using her support skill.
The game recommends Rock Python as her best 4* weapon, but it isn't.
Rock Python provides a weaker ATK buff than Lapis Lazuli.
Rock Python's buff lasts 7 seconds, whereas Lapis Lazuli's buff lasts 15s.
(Eatchel's Support Skill has a 12s cooldown.)
Rock Python is much worse than Lapis Lazuli.

For weapon Parts, just go with ATK, as her healing scales off her ATK.

Logistics

Use Lux squad - it was designed specifically for her and is her best choice as it gives a stacking extra Healing Bonus.

Note that the stacks are removed 2 seconds after Eatchel uses any skill.
This is because Eatchel's support skill causes her to leap and deal damage, and then return, with her healing occuring after she returns from her leap.
Eatchel fully returns from her leap 1.1 seconds after her support skill is used.
As such, the 2s delay on Lux squad is there to allow the stacking Healing Bonus to apply to actually Eatchel's support skill, as if it was removed immediately on using her support skill then the stacks would be removed before Eatchel returned and healed, so she wouldn't gain the bonus.

Ideal [endgame] Stats if Eatchel has her 5* weapon

For the Special talent, Eatchel wants +10.6% Healing Bonus (note: Healing Bonus affects healing done, not healing received).
For basic stats, Eatchel's ideal stats are +10.0% ATK and +106 Alignment Index.

Ideal Stats if Eatchel doesn't have her 5* weapon yet

If Eatchel does not have her 5* weapon (Blitzing Fangs) then Skill Haste and S-Energy Recovery are also good rolls.
Since you'll ideally get Blitzing Fangs eventually though, it's not worth giving Eatchel non-Alignment rolls, as you'll need to re-roll them into Alignment Index rolls once you get Blitzing Fangs, so you're better off just going for Alignment Index to begin with so you don't waste the re-rolls later on.

Stats Explanation - Ideal Endgame Stats

Healing Bonus is the only useful Special stat Eatchel can have.
Her healing scales off of her ATK, so ATK is her most useful stat.
Alignment gives her more Healing Bonus, which is good.

Since Eatchel ideally never uses her support skill, and thus never deals damage, +Kinetic Damage is useless to Eatchel.
Since skills can't crit, crit rate/dmg mods are also useless to Eatchel.
U-Energy recovery is not useful for Eatchel to have either.

Good stats if using her 4* weapon:

Eatchel's support skill uses 12 S-Energy on a 12s cooldown, so she has no S-Energy issues even if she spams her support skill off-cooldown
If Eatchel has Skill Haste though, she can use more S-Energy than she recovers, so without any S-Energy recovery mods she'll eventually run out of S-Energy.
As such, if Eatchel has Skill Haste, a corresponding S-Energy Recovery mod can be useful for longer fights so she doesn't run out of S-Energy.
In practice your fights shouldn't last that long, so S-Energy is a very weak mod for Eatchel, but it can, technically speaking, be useful for her if she doesn't have Blitzing Fangs.

If Eatchel doesn't have Blitzing Fangs yet, then you can spam Eatchel's support skill off-cooldown in order to proc the buffs from the 4* weapons Rock Python and Lapis Lazuli, in which case giving Eatchel Skill Haste rolls will allow her to use her support skill more often, increasing the amount of healing she does.
Skill Haste will also increase the %uptime on Rock Python's buffs, as it's a 7s buff, and Eatchel's support skill has a 12s cooldown by-default.
With Lapis Lazuli, you only need to use her support skill every 15s to maintain Lapis' buff, but Skill Haste means her support skill comes off cooldown sooner, allowing for more passive healing between support skill casts.

Given that you'll ideally get Blitzing Fangs eventually, it is, again, better to go for Alignment Index to begin with, rather than going for Skill Haste/S-Energy and then needing to re-roll for Alignment Index later when you do get Blitzing Fangs.

Manifestation

With M1 and a Kinetic Weapon equipped, Eatchel always has 2 Icebound Claws, and if she has 2 or fewer Icebound Claws they no longer naturally disappear.
This means that with M1, Eatchel will always have 2 Icebound Claws active, each of which provides the usual passive ATK buff to the entire squad.
M2 decreases the cd of Eatchel's ult from 60s to 30s.
Given that Eatchels ult is generally quite weak, you're normally better off using the ult of another operative.
There are very few combinations of operatives where you'd actually want to use Eatchel's ult.
Since Eatchel's ult is pretty weak, reducing the cooldown of her ult is not overly useful, and thus M2 is generally very weak.
M3 increases damage by 3% per Claw.
Given that her M1 gives her two claws permanently, this is at least a 6% damage boost for the squad, which isn't much, although it is entirely passive.
There aren't many squads where you want to use Eatchel's ult, but for those squads M3 is a larger bonus and is a decent buff, as her ult can give her a lot of claws.
M4 increases the level of Eatchel's ult skill by 1, increasing its healing and damage.
M4 increases the capacity of Eatchel's Icebound Claws to (35% of her ATK +195), up from (30% +180) (Around 1,680 -> 1,945. Around 15% more.)
15% more Icebound Claw capacity means 15% more ATK buff, so this is a buff to Eatchel's passive ATK buff.
This is not a massive buff to Eatchel's support capabilities, but it does buff them.
M5 increases the max number of Icebound Claws by 1.
This doesn't affect how much she buffs the squad unless she uses her ult, so for most team compositions (where you don't use Eatchel's ult) M5 isn't useful.
This makes M5 a very niche pick, as it's only useful on the very small number of squads where Eatchel can actually use her ult.

If you want efficiency (good damage with minimal investment), then M1 is a good stopping point.
For almost all team compositions and scenarios, M1 is generally all you need to give Eatchel, but M1 is very strong for her and you should always get Eatchel to M1.

M3 and M4 do increase Eatchel's capabilities as a support operative, but they are small buffs that require huge investment, as getting them requires getting M2, which is useless for most team compositions.
Since Eatchel is generally never an operative whose ult you want to use, M5 is overkill in all but a few niche scenarios or for a few specific team compositions.

Which Main-DPS to pair with Eatchel?

Eatchel's healing can be appreciated by literally every other operative in the game without exception.

Eatchel's ATK buffs are appreciated by almost every every main DPS.
Similarly, since Eatchel doesn't deal any damage, she doesn't get in the way of type-specific buffs, most notably Vidya - Celestial Swan.
This makes Eatchel something of a universal support - she can be used on basically every team.

Eatchel thus works well as a general support for all operatives, with only a small number of exceptions:

Clarina - Crimson Moon
Clarina gains extra Skill DMG based upon the amount that she is healed by [from any source], meaning Eatchels healing gives Clarina extra Skill DMG, which means that Eatchel provides Clarina with more buffs than she does for any other operative, meaning Eatchel is generally Clarina's best support.
Nita - Pulse
Pulse's damage scales off of her Max HP, not her ATK, which Eatchel doesn't affect.
As such, Eatchel's ATK buffs are useless for Nita - Pulse, although Pulse can still make use of Eatchel's passive healing.
Yao - Nightglow
Nightglow's damage scales off of her DEF, not her ATK, which Eatchel doesn't affect.
As such, Eatchel's ATK buffs are useless for Nightglow, although since Nightglow is only useful as a support operative this isn't really an issue.
Siris - Freefin
Freefin's buffs scale based off of her Max HP, not her ATK, which Eatchel doesn't affect.
As such, Eatchel's ATK buffs are useless for Freefin, although since Freefin is primarily a support operative this isn't much of an issue.

4* Weapons: Healing and Damage Maths: Skill Haste, Alignment Index, and using her Support Skill

Note: Contains maths.
The TL:DR is that you should just get 3x Alignment Index rolls and not bother with S-Energy Regen or Skill Haste mods.

Blitzing Fangs:

Eatchel's 5* weapon - Blitzing Fangs, gives an ATK buff based on how much total healing was done in the last 20s, which continuously decreases.
Maintaining the maximum buff from Blitzing Fangs is quite easy with Eatchel's passive healing, and once maxed Blitzing Fangs' buff will remain maxed from the Passive healing alone.
If spamming her support skill, then Blitzing Fangs will give a varying ATK buff, as the infrequent healing from Eatchel's support skill means the buff will decrease each second between casts, leading to a fluctuating ATK buff.
This means that Eatchel's passive healing gives a higher average ATK buff from Blitzing Fangs when compared to spamming her support skill.
This means that Eatchel performs best when she has Blitzing Fangs and is performing passive healing, and never uses her support skill.

You can use her support skill to get a higher Blitzing Fangs buff for the first few seconds of combat, but beyond those first few seconds the buff gained from her passive healing is stronger.

Lapis Lazuli performs the same regardless of how Eatchel heals, and Rock Python performs best with max Skill Haste, but neither are anywhere near as good as Blitzing Fangs.
Again: Blitzing Fangs is Eatchels best weapon by a huge margin.

If you don't have Blitzing Fangs:

Eatchel's Support Skill passively heals for (5% ATK +37) each second, and using her Support Skill heals for (60% ATK + 446) on a 12s cooldown.
This means that in-theory Eatchel should heal the same regardless of whether she stays off-field to provide passive healing or if she spams her support skill.
In practice though, there are several differences:

Eatchels Support Skill goes off-cooldown only after she returns from her pounce, not when she actually uses her support skill, so using her support skill actually takes over 12s in total, leading to her using her support skill having lower average base healing than her passive healing.
Eatchel needing to return after her pounce adds 1.1 seconds to the total time it takes her to use her support skill.
(This is why the Lux logistics squad removes Winter Fleece stacks 2s after using a skill - it's to allow Eatchel to use her support skill and still have it heal at full WF stacks.)
If you go Skill Haste, then Eatchel can use her Support Skill more often, but if she uses her Support Skill more often than every 10s then she won't be at max Winter Fleece stacks from her Lux logistics squad, leading to reduced healing.
This affects her when she has 2x and 3x Skill Haste rolls, but not 1x Skill Haste.
Similarly, going Skill Haste means she can't take Alignment Index, and thus doesn't gain the extra +6.36% Healing Bonus from each [max-roll] Alignment Index stat.
When given any Skill Haste mods, Eatchel will be using more S-Energy than she recovers, meaning she'll eventually run out of S-Energy.

If spamming her support skill off-cooldown, then giving Eatchel Skill Haste rolls will thus lead to Eatchel doing less-buffed healing more often.

Factoring in the extra time Eatchel takes to return from her pounce, then assuming Lux + Blitzing Fangs + N6/D4 and doing the maths gives the following average values for how much healing Eatchel does per second, as a percentage of her ATK stat.
The asymptote number shows her average healing after her S-Energy runs out and her healing becomes limited by her S-Energy regen rather than her skill cooldown:
Healing/s (% ATK) Asymptotes towards Logistics rolls Healing method

11.57% 11.57% (no change) 3x Alignment Index + 0x Skill Haste rolls Only passive healing (i.e. she never uses her support skill)
10.60% 10.60% (no change) 3x Alignment Index + 0x Skill Haste rolls Spamming her support skill off-cooldown (and thus no passive healing)
12.03% 11.19% 2x Alignment Index + 1x Skill Haste Spamming her support skill off-cooldown (and thus no passive healing)
13.20% 10.73% 1x Alignment Index + 2x Skill Haste Spamming her support skill off-cooldown (and thus no passive healing)
13.84% 10.03% 0x Alignment Index + 3x Skill Haste Spamming her support skill off-cooldown (and thus no passive healing)
11.62% 11.62% (no change) 1x Haste, 1x Alignment, & 1x S-Energy Regen Spamming her support skill off-cooldown (and thus no passive healing)

As such, spamming Eatchels Support Skill can result in her doing more healing on average when compared to her passive healing, but it depends on how she is built.

For longer fights where her healing is limited by her S-Energy Recovery speed, you could either go 3x Alignment Index and let her heal passively, or you can go 1x Haste, Alignment, and S-Energy Recovery and spam her Support Skill off-cooldown.
Both of these perform almost identically in terms of healing.
Whilst the active method has a higher number above, in practice you won't always be able to use her support skill the nanosecond it comes off-cooldown, and the passive healing will heal for slightly more on-average because of that, but they're extremely similar.

With 3x Skill Haste rolls, Eatchel uses 12 S-Energy every 8s or so, meaning she will eventually run out of S-Energy, preventing her from spamming her support skill.
Due to the extra 1.1s delay of Eatchel needing to return from her pounce after using her support skill, 1x Skill Haste +1x S-Energy Recovery does allow her to sustain her support skill indefinitely.

When Eatchel runs out of S-Energy, the rate at which her support skill can be used is entirely limited by her S-Energy regen.
If Eatchel has run out of S-Energy, then her best method of healing is just passively healing with 3x Alignment rolls or spamming her support skill with 1 each of Alignment, Skill Haste, and S-Energy Recovery, which perform almost identically.
If you aren't using Blitzing Fangs though then you're better off spamming her support skill to proc her weapon buff (Lapis Lazuli or Rock Python)

Again, using Blitzing Fangs with her passive skill is the best way of using Eatchel, but 1x Skill Haste + 1x Alignment Index + 1x S-Energy are good stats if you don't have Blitzing Fangs yet, although since you'll want to get 3x Alignment Index when you do get Blitzing Fangs it's not worth re-rolling for any non-Alignment stats as you'll just need to re-roll them later anyway - Eatchel heals for so much that the extra healing you get from spamming her support skill more often isn't overly useful.