Here is the full list of all 15 Guild of Ascension achievements.
Reach the Forest biome within the Tower.
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 5 items within any shop.
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.