Here is the full list of all 15 Guild of Ascension achievements.
Reach the Forest biome within the Tower.
Buy a total of 5 items within any shop.
Reach the Mountain biome within the Tower.
Reach the Swamp biome within the Tower.
Defeat a total of 100 enemies in the Tower.
Defeat a total of 500 enemies in the Tower.
Defeat a total of 1000 enemies in the Tower.
Buy a total of 10 items within any shop.
Buy a total of 15 items within any shop.
Collect a total of 1000 Exp point within the Tower.
Collect a total of 5000 Exp point within the Tower.
Collect a total of 15000 Exp point within the Tower.
Run a total of 800 tiles within the Tower.
Run a total of 4000 tiles within the Tower.
Run a total of 12000 tiles within the Tower.