Here is the full list of all 6 The Ouroboros King achievements.
Defeat Edea, the Witch Queen to unlock this achievement. You can find her at the Capital.
Defeat Thabita, the Deceptive to unlock this achievement. You can find her at the Tower of Trickery.
Defeat Andromeda of the Stars, to unlock this achievement. You can find her at the Castle of the Coven.
Defeat the Coven and stop their plans.
Defeat the Coven 5 times to save Thessalonia.
Defeat the Coven at 30 difficulty.