Here is the full list of all 16 Dark Tower achievements.
You complete the game
You complete level 15
You complete level 14
You complete level 13
You complete level 12
You complete level 11
You complete level 10
You complete level 9
You complete level 8
You complete level 7
You complete level 6
You complete level 5
You complete level 4
You complete level 3
You complete level 2
You complete level 1