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