Here is the full list of all 16 Ys VI: The Ark of Napishtim achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Complete Boss Rush mode on any difficulty.
Destroy the Ark’s Central Shaft.
Defeat Ernst.
Acquire all equipment.
Acquire every Tabulas.
Defeat Orjugan.
Defeat Ud-Meiyu.
Defeat Zonplas.
Win the duel with Geis.
Defeat the Wandering Calamity.
Win a boss fight without taking a single hit.
Defeat Majuunun.
Win a boss fight with 1 HP remaining.
Complete the game on Nightmare difficulty.
Complete the game in Catastrophe Mode.
Obtain every other achievement.