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