Here is the full list of all 13 Tower Numbers achievements.
Complete level 5
Complete level 10
Complete level 15
Complete level 20
Complete level 25
Complete level 30
Complete level 35
Complete level 40
Endless mode 50
Endless mode 100
Got a score of 400 in classic mode
Got a score of 800 in classic mode
Got a score of 1600 in classic mode