Guide
How the kit works
Start by pressing Icetide Vortex and hitting an opponent to gain a Grimheart stack. Eula can hold up to two stacks, which increase her DEF and resistance to interruption. Stacks can be gained once every 0.3s.
Cast Glacial Illumination next. It deals Cryo DMG and creates a Lightfall Sword for up to 7s. Casting it resets the cooldown of Icetide Vortex and gives Eula one Grimheart stack, so a successful press before the Burst gives her two.
Hold Icetide Vortex to consume those stacks. The hold deals AoE Cryo DMG, lowers nearby opponents' Physical RES and Cryo RES when stacks are consumed, and turns each stack into an Icewhirl Brand that deals Cryo DMG. Consuming two stacks also creates a Shattered Lightfall Sword, which explodes for 50% of the basic Physical DMG of a Lightfall Sword.
Keep attacking with Favonius Bladework - Edel (NA) while the main sword is present. Eula's Normal Attack, Skill and Burst damage can charge it, with at most one energy stack gained every 0.1s. It explodes when its duration ends, dealing more Physical DMG based on the stacks. Switching Eula out makes it explode immediately.
Build and why
Song of Broken Pines is the first weapon to consider. It gives 16% ATK, and Normal or Charged Attack hits build Sigils. At four Sigils, nearby party members gain 12% Normal ATK SPD and 20% ATK for 12s. Both bonuses suit the time Eula spends attacking.
Gest of the Mighty Wolf gives 10% ATK SPD. Normal Attack hits and skill casts build its damage bonus, up to four stacks. The extra CRIT DMG on that effect requires the party's Hexerei: Secret Rite effect. Beacon of the Reed Sea is another option: a skill hit grants 20% ATK for 8s, and taking damage grants a separate 20% ATK effect for 8s. Akuoumaru is a four-star alternative that increases Burst damage based on the party's combined maximum Energy capacity.
Use four pieces of Pale Flame. Its two-piece bonus gives 25% Physical DMG, and skill hits build ATK stacks. At two stacks, the Physical DMG bonus doubles. If you do not have four suitable pieces, use two Pale Flame and two Bloodstained Chivalry for 50% Physical DMG in total. Four Gladiator's Finale is another option, with 18% ATK and 35% Normal Attack DMG for a Claymore user.
Choose ATK Percentage or Energy Recharge on the sands, Physical DMG Bonus on the goblet, and CRIT Rate or CRIT DMG on the circlet. For substats, look for CRIT Rate, CRIT DMG, Energy Recharge and ATK Percentage, in that order. Energy Recharge helps you prepare the next Burst; the other stats support her damage.
Leveling priority
My suggested talent order is Glacial Illumination, Favonius Bladework - Edel (NA), then Icetide Vortex. The Burst creates Eula's large Physical DMG hit, while Normal Attacks are used throughout her field time and charge the sword. The skill still matters for its RES reduction and Grimheart use.
For ascension, gather Dandelion Seed, Crystalline Bloom, Shivada Jade Sliver, Shivada Jade Fragment, Shivada Jade Chunk and Shivada Jade Gemstone. You also need Damaged Mask, Stained Mask, Ominous Mask and Mora.
Talent upgrades use Teachings of Resistance, Guide to Resistance, Philosophies of Resistance, the same three mask materials and Mora. Higher upgrades also need Dragon Lord's Crown and Crown of Insight. When Eula crafts Character Talent Materials, she has a 10% chance to receive double the product.
Constellations worth it
Tidal Illusion is the first constellation to look at. Consuming Grimheart gives Eula 30% Physical DMG for 6s, with each stack consumed adding 6s to the duration, up to 18s. It fits the hold skill she already uses before her sword explodes.
Noble Obligation is also worth considering: the Burst sword starts with five energy stacks, and Normal Attacks, Skills and Bursts have a 50% chance to grant an extra stack. Lawrence Pedigree adds three levels to the Burst, up to level 15.
Lady of Seafoam makes the hold skill's cooldown equal to the press cooldown, but you can skip it if that convenience is not important to you. The Obstinacy of One's Inferiors only increases Lightfall Sword damage against opponents below 50% HP. Chivalric Quality adds skill levels, so it is less directly focused on the Burst sword than C3.
Common mistakes
Do not switch Eula out by accident while her Lightfall Sword is charging. It explodes immediately, so you lose the remaining time you could have used to build stacks. Stay close to opponents and keep landing hits.
Do not hold Icetide Vortex without checking your Grimheart stacks if you want its RES reduction and the extra sword from consuming two stacks. Use the Burst's cooldown reset and granted stack to help set that up.
Do not focus only on Cryo damage when choosing artifacts. The main Lightfall Sword deals Physical DMG, so Physical DMG Bonus has a clear use. Also leave room for Energy Recharge if you need help preparing the next Burst.