Enya - Tempest is currently not available as a trial operative in any story mission.
Tempest deals very good AoE damage as well as single-target damage, and has good mobility, but needing to be near to enemies to deal damage makes her extremely squishy, and she can be quite difficult to teambuild, especially if you don't have Vidya - Celestial Swan or Tess - The Magician.
Role: Main DPS
Kinetic Damage
Deals entirely skill damage
Mobility is a mixed bag
Massive amounts of AoE
Extremely high burst damage
Good DPS, especially single-target
Dodge can give incredible mobility
Sustained damage is relatively mediocre
Low mobility can make her extremely squishy
Dear lawd she do be squishy...
Low mobility during normal gameplay
Never shoots her gun
This is problematic for many support effects
1. If you have max U-Energy, use your Ult.
You can use Tess - The Magician to charge her Ult instantly, dealing absolutely massive burst damage, which is one of Tempest' main strengths.
2. If your standard skill has max Wind Power, then hold your Standard Skill to use it.
3. If you need to gap-close, then use Tempests dodge.
4. Otherwise just use your standard skill.
Note that this doesn't ever actually using your gun - you never need to fire it at all, and never should.
Again, use your dodge if you need to close a gap - it's much faster, so you should never need or have an opportunity to shoot.
Passive Effect
Tempest's dodge turns her into a Vortex.
This knocks enemies up, pulls them towards/into her, and deals damage.
This allows Tempest to group up enemies using her dodge, which can be quite useful for grouping strong non-boss mobs.
Tempests' dodge allows her to move very quickly, allowing her to have excellent mobility [at least in theory].
If any of Tempests skills hits less than 5 targets, it deals +37.5% damage per target less than 5.
This is obviously a huge damage boost against single-targets (i.e. bosses).
Standard Skill
Tap the Standard Skill key to have Tempest creates a PBAoE vortex.
This knocks enemies up and deals good damage, whilst also generating Wind Power.
Hold the Standard Skill key to have Enya create a much larger and stronger PBAoE vortex. This can be sustained as long as Tempest has Wind Power.
Whilst Tempest is in either type of vortex, she can't be interrupted.
Tempest can move while a standard skill vortex is active, but she is extremely slow.
This very poor mobility can make Tempest extremely squishy, as the low range of her standard skill means she needs to stand very close to enemies, which makes it hard for her to move out of the way of enemy attacks whilst not crippling her own DPS by stopping her standard skill in order to dodge.
Ultimate Skill
Tempest uses all U-Energy to deal massive AoE damage based on how much U-Energy she uses.
Due to Tempests passive effect, this is best used against single-targets.
Using Tess - The Magician to charge and instantly use Tempest's Ult is [with a good debuffer] often enough to one-shot many bosses
Especially alongside a strong resistance-shredder like Celestial Swan.
Once that initial burst is over, her dps does drop off though.
Support Skill
Tempest creates an AoE that carries operatives upwards, effectively acting as a raised platform.
Enemies are pushed back from it, and damaged the first time they touch it.
Like most Main-DPS-ers, you really don't want to use Tempest as a support operative.
Amethyst Thorns
Her 5* weapon, and her best weapon.
Like most 5* weapons, the weapon increasing the damage enemies take is very strong, and is the 5*'s main advantage.
Swamp Snapper
Her 4* event weapon. Better than anything else.
For weapon Parts just go with ATK.
Use Gleam squad - it was designed specifically for her and is her best choice.
For stats you want +10.0% ATK and +106 Alignment Index.
For the Special talent, you want 8.5% Kinetic Damage
Alignment gives her more ATK.
Since skills can't crit, and skills are the only thing she uses, crit [rate and damage] mods are useless for her.
All skills other than ATK and Alignment Index are worthless.
M1 - +25% Skill DMG when equipped with a Kinetic Weapon (i.e. always), as well as +25% Wind Power gained.
M2 - Reduces the DEF of enemies hit during her Standard Skill by 5% for 2s, up to 20%.
M3 - When equipped with a Kinetic Weapon (i.e. always), Enya's skills ignores 15% of the enemies Kinetic Resistance.
M4 - Standard Skill level +1, and increases the damage by around 10%.
M5 - After Tempest deals damage with her Standard Skill or dodge, increases the damage of her next Engulfing Vortex (holding standard skill)
M5 for max damage.
If you don't want to get Tempest all the way to M5, then M3 is a good stopping point.
Vidya - Celestial Swan (and other resistance shredders)
Celestial Swan and other resistance shredders (Acacia - Kaguya, etc.) that reduce the enemies resistance help enemies take more damage.
If using Celestial Swan, make sure the other support isn't off element to the main DPS.
Marian - Riptide
Enya benefits from Marians Skill DMG and ResPen buffs
Being off-element means that Riptide is not a good choice if used with Celestial Swan, but otherwise Marian works well.
Eatchel - The Cub
A Blitzing Fangs Eatchel provides a nice ATK boost, as well as the passive healing.
Given that Tempest needs to be near enemies to deal damage, she can be quite squishy, which Eatchel massively helps with.
Tess - The Magician
Tempests ult is extremely strong, and having Tess give quicker and more frequent access to Tempests ult, increasing her damage a lot.
Note that Tempest gains buffs after using her standard skill, so don't just ult immediately - use her standard skill for 4s to buff Tempest before using her ult.
Cope Supports - I.e. you don't have the above, but you want her to have something:
Mauxir - Shadow Ka
Being an AoE character Shadow Ka's utility is mostly useless, however the extra damage is nice.
Nightglow
Whilst her Ballistic and Crit buffs are useless, her ATK bonus is still good.
Agave - Basically a passive 20% ATK bonus. Decent, but not quite as strong as the above.
A 15s buff on a 15s duration means it has basically 100% uptime though.
Enya - Exuvia
Tempest doesn't shoot, which is a problem for Exuvia, but the bonuses are ok if you don't have a better support.