Here is the full list of all 49 ToeJam & Earl: Back in the Groove trophies - there are 40 bronze, 5 silver, 3 gold and 1 platinum.
Hit and leave through the very first exit in the Hyper Funk Zone
Reach the end of the HyperFunk Zone
Get a game over before level 3
Beat normal or hard world without dying
Beat normal or hard mode without popping a single Earthling
Beat normal or hard world without opening a single present
Play as each of the playable characters
Complete hard world
Collect all of the locked presents
Pop 8 or more Earthlings who are dancing at a boombox in one game
Get killed by a Little Girl with a Teddy
Send an identified bad present to another player
Play as both old Skool TJ and as Old Skool Earl
Complete a random world game
Reach the rank of FunkLord
Open the Total Bummer twice in one game
Pop at least one of every bad Earthling type in one game
Use The Boom Box 4 times in one game
Uncover all the map tiles for 3 levels in one game
Pop a mole who has stolen one or more of your presents
Make other player snap out of being in love by slapping them
Complete a fixed world game
Open an unidentified Major Randomizer, Total Bummer, or Instant Demotion after level 20
Give a life to another player 3 times in one game
Open the Major Randomizer or Baby Randomizer 3 times in one game
Use Heal Friend Present on another player 10 times in one game
Make other player wake up by shouting at them
Get hit by Cupid's arrow 5 times in one game
Get to hot tub island
Complete the game with a friend
Save yourself from burning up by jumping in water
Catch Santa 3 times in one game
Catch 5 elves in one game
Beat the 5th level in Rhythm Matching
Visit a backer character
Go for a ride in the Evil Elevator twice in one game
Successfully open 10 broken presents in one game
Have at least 99 bucks
Hide in sunflowers 4 times in a game when being chased by an Earthling
Collect a locked present
Fall off current level 5 times in one game
Hi Five another player 3 times in one game
Get to secret Funkotron Level via a secret doorway
Open unidentified presents 15 or more times in one game
Eat every type of food in one game
get all the trophies in the game
Have 10 broken presents blow up on you in one game
Unlock all power hats
Visit every backer character