Here is the full list of all 10 Space Pirate Trainer achievements.
Win the Game
Get a multiplier combo of 12
Reach wave 20 without using a Shield
Destroy the Ray Boss
Pull a droid into its own laser
Destroy your first Heavy Droid
Reach wave 10
Destroy the Mother Droid
Zap 25 droids with the Tesla Coil in one game
Survive wave 23 for one minute without using your Gun, Shield or Volton