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