Here is the full list of all 10 Mutant Mudds Deluxe trophies - there are 5 bronze, 4 silver and 1 gold.
Unlock all characters
Collect all of Grannie's medals
Collect all known water sprites and golden diamonds
Beat the game. You'll know it when you see it.
Collect 4000 golden diamonds, unnecessarily
Collect all the spooky water sprites
Unlock the path to space
Beat a REAL level without using the checkpoint (1-1 doesn't count!)
Beat a REAL level without getting hit (1-1 doesn't count!)
Beat a REAL level without dying once (1-1 doesn't count!)