Here is the full list of all 13 Mutant Mudds Super Challenge achievements.
Beat a level with checkpoints disabled
Get killed by spikes or lava
Go skydiving and survive
Get killed by a bomb as Bomb Monkey
Try to escape the Final Boss by boosting to the roof
Collect one special character using another
Avoid killing any bad guys in a level where that's actually a challenge
Collect all songs
Beat final boss without getting hit
Beat a level with no gems.
Beat the game
Collect all the characters
Beat the game with less than 100 deaths