Here is the full list of all 12 Gnumz: Masters of Defense achievements.
Destroy 10,000 enemies
Earn 240 stars
Upgrade any spell to the maximum level
Complete a level with only one piece of ore remaining
Use 200 spells
Complete all levels of any episode with 3 stars
Lose 3 times in a row
Destroy 5,000 enemies
Only one enemy attacked the base
Buy all the upgrades for one of the traps
Complete a level without using spells
Destroy 1,000 enemies