Here is the full list of all 20 Puzzle Tactics achievements.
Complete level 1.
Complete level 2.
Complete level 3.
Complete level 4.
Complete level 5.
Complete level 6.
Complete level 7.
Complete level 8.
Complete level 9.
Complete level 10.
Complete level 11.
Complete level 12.
Complete level 13.
Complete level 14.
Complete level 15.
Complete level 16.
Complete level 17.
Complete level 18.
Complete level 19.
Complete level 20.