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