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