Guide
How the kit works
Start by applying Riptide. A fully charged Aimed Shot from Cutting Torrent (NA) marks its target. You can instead use Havoc: Obliteration in Ranged Stance: it deals AoE Hydro DMG, applies Riptide and returns part of its Energy Cost.
Use Foul Legacy: Raging Tide to enter Melee Stance. Its Normal and Charged Attacks deal Hydro DMG, and the Charged Attack consumes Stamina. Hitting a marked enemy with a melee attack triggers Riptide Slash, dealing AoE Hydro DMG counted as Elemental Skill DMG. It can trigger once every 1.5s.
In Melee Stance, the passive Sword of Torrents lets CRIT hits from Normal and Charged Attacks apply Riptide. Never Ending extends the status by 8s. When a marked opponent is defeated, Riptide Burst spreads the status to nearby opponents it hits.
If you use Havoc: Obliteration in Melee Stance, it deals AoE Hydro DMG and triggers Riptide Blast on marked targets, clearing their marks. End the stance manually before you stay in it too long. It ends automatically after 30s, with an even longer cooldown.
Build and why
Use four pieces of Nymph's Dream. Its two-piece bonus gives 15% Hydro DMG Bonus. Hits from different attack types build independent stacks; at three or more stacks, the set gives 25% ATK and another 15% Hydro DMG Bonus. Tartaglia can build stacks with attacks, his Skill and his Burst.
Four pieces of Heart of Depth are the next option: after using the Skill, Normal and Charged Attack DMG increases by 30% for 15s. Four pieces of Shimenawa's Reminiscence are another choice, giving 50% more Normal, Charged and Plunging Attack DMG for 10s after the Skill consumes 15 Energy. For a mixed set, use two pieces each of Heart of Depth and Gladiator's Finale for Hydro DMG Bonus and ATK.
Choose ATK Percentage on the sands, Hydro DMG Bonus on the goblet, and CRIT Rate or CRIT DMG on the circlet. Look for CRIT Rate and CRIT DMG in substats first, followed by ATK Percentage, Energy Recharge and Elemental Mastery. CRIT Rate also helps apply Riptide through Sword of Torrents.
Polar Star is the first weapon choice: it boosts Skill and Burst DMG and gives ATK stacks for hits from different attack types. Aqua Simulacra increases damage when opponents are nearby. Thundering Pulse gives ATK and can increase Normal Attack DMG, with stacks tied to Normal Attack hits, Skill use and Energy.
Leveling priority
I'd level Foul Legacy: Raging Tide first because it covers the melee stance and Riptide Slash. Put Havoc: Obliteration second for its damage in both stances. Level Cutting Torrent (NA) after that: it covers bow attacks and Riptide Flash, whose damage counts as Normal Attack DMG.
For ascension, gather Mora, Starconch and Cleansing Heart, along with Varunada Lazurite Sliver, Varunada Lazurite Fragment, Varunada Lazurite Chunk and Varunada Lazurite Gemstone. You also need Recruit's Insignia, Sergeant's Insignia and Lieutenant's Insignia.
Skills use the same three Insignia materials and Mora, plus Teachings of Freedom, Guide to Freedom, Philosophies of Freedom, Shard of a Foul Legacy and Crown of Insight. Maxing all three skills takes three Crown of Insight.
Constellations worth it
My pick for the biggest upgrade is Havoc: Annihilation. Casting Havoc: Obliteration in Melee Stance resets the cooldown of Foul Legacy: Raging Tide, though the reset takes effect only after Tartaglia returns to Ranged Stance.
Next, Foul Legacy: Tide Withholder reduces the Skill cooldown by 20%. Abyssal Mayhem: Vortex of Turmoil adds three Skill levels, making it a good choice if you want to invest further in his melee kit.
Abyssal Mayhem: Hydrospout is worth considering for extra Riptide triggers every 4s, with separate intervals from the usual effects. You can also skip Foul Legacy: Understream, which restores 4 Energy when a marked enemy is defeated, and Havoc: Formless Blade, which adds three Burst levels. None is needed to use the base kit.
Common mistakes
Don't stay in Melee Stance until it ends automatically unless you are prepared for the longer cooldown. Switch it off yourself and use that time for the rest of the team. Also remember that Tartaglia cannot perform a Plunging Attack in this stance.
Don't use the melee version of Havoc: Obliteration expecting it to preserve Riptide: Riptide Blast clears the status from marked targets it hits. Reapply it with a CRIT hit in Melee Stance or use a ranged application.
Don't equip four pieces of Gladiator's Finale for its Normal Attack bonus. That effect requires a Sword, Claymore or Polearm, while Tartaglia uses a Bow. Its two-piece ATK bonus is still usable in a mixed set.