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