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