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