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