Here is the full list of all 20 Tomb of Tyrants achievements.
Kill a hero with your Tyrant.
Fulfill 50 prophecies (cross-session).
Complete 20 plots in a single session.
Defend a floor with three max-level minions in one battle.
Reach wave 25.
Earn a level 10 minion.
Earn 10 level-5 minions in a single session.
Fulfill 25 prophecies (cross-session).
Reach wave 10 without spending resources on minions.
Achieve a 3x multiplier.
Achieve a 5x multiplier.
Construct a 20-floor dungeon.
Complete 30 rituals in a single session.
Stockpile 50 of a single resource at one time.
Reach wave 10.
Use 20 potions in a single session.
Without using items, achieve a 2x multiplier on a single resource match.
Construct a 10-floor dungeon.
Fulfill 75 prophecies (cross-session).
Acquire 5 corrupted heroes at once.