Here is the full list of all 12 Mutant Mudds Super Challenge trophies - there are 7 bronze, 4 silver and 1 gold.
Collect all songs
Beat the game
Beat the game with less than 100 deaths
Beat final boss without getting hit
Try to escape the Final Boss by boosting to the roof
Collect all the characters
Get killed by a bomb as Bomb Monkey
Beat a level with no gems
Avoid killing any bad guys in a level where that's actually a challenge
Collect one special character using another
Beat a level with checkpoints disabled
Get killed by spikes or lava