Here is the full list of all 15 The Tower Of Elements achievements.
Upgraded the Tower to maximal level
Collected 45000 Mana Point in Total
Unlocked all other achievements
Collected 20000 Mana Point in Total
Unlocked 10 Mages
Unlocked 5 Mages
Unlocked 1 new Mage
Got 1300 Points
Upgraded the Tower 20 times
Collected 4000 Mana Point in Total
Got 1000 Points
Made 200 Combo
Got 500 Points
Made 100 Combo
Upgraded the Tower 10 times