Here is the full list of all 8 Curvatron achievements.
Finish every level in the Adventure mode
Get 4000 points in Evergrowing mode
Finish a community level
Get 30 points in Classic mode, collecting all shrink powerups
Get 30 points in Classic mode without collecting any shrink powerups
Have two players kiss in Multiplayer mode
Take a bite out of yourself
Finish every Hardcore level