Here is the full list of all 23 Destiny or Fate achievements.
Finish the story with all heroes.
Gain 1,000,000 golds.
Finish the story with ten heroes.
Finish the story with five heroes.
Gain 10,000 golds.
Slay 1000 normal monsters.
Slay 50 elites.
Slay boss, Scythe.
Slay boss, Zatorich.
Finish the story with one hero.
Slay boss, Skeleton King.
Slay boss, Yacha.
Complete Chapter.3
Complete Chapter.2
Slay boss, Hydra.
Improve your hero via Enchant Point
Get mastery for the first time.
Slay boss, Draga.
Defeat for the first time.
10 Defeats.
Complete Chapter.1
Slay first elite.
Arrive in shop block for the first time.