Here is the full list of all 9 Toy Tanks achievements.
Complete your first level
Defeat the first boss
Defeat the second boss
Beat a level with less then 1HP left
Create your own level
Defeat the third boss
Collect 3 Stars on Hard for all standard levels
Beat a major Boss(1-10, 2-10, 3-10) without shooting
Complete your Adventure(A-1 to A-20)