Here is the full list of all 56 Freedom Planet achievements.
Clear Adventure Mode with over 7000 crystal shards
Collect all 10 cards in Pangu Lagoon
Clear all target rooms in Shang Mu Academy as Carol
Clear all target rooms in Shang Mu Academy as Milla
Clear all target rooms in Shang Mu Academy as Lilac
Collect all 10 cards in Thermal Base
Collect all 10 cards in Relic Maze
Collect all 10 cards in Jade Creek
Collect all 10 cards in Fortune Night
Collect all 10 cards in Aqua Tunnel
Collect all 10 cards in Trap Hideout
Collect all 10 cards in Sky Battalion
Clear Pangu Lagoon in 8 minutes
Clear Thermal Base in 9 minutes
Clear Trap Hideout in 6 minutes
Destroy both of the Mantalith's arms before the fight begins
Play the Secret Melody on a piano
Collect all 10 cards in Battle Glacier
Collect all 10 cards in Dragon Valley
Clear Sky Battalion in 7 minutes
Clear Aqua Tunnel in 5 minutes
Clear the game without losing any lives
Clear the game in less than 90 minutes
Clear Final Dreadnought 2 in 9 minutes
Clear Battle Glacier in 12 minutes
Clear Jade Creek in 8 minutes
Clear Sky Battalion without using Torque's plane
Clear Relic Maze in 8 minutes
Skip the Claw boss in Relic Maze
Clear Dragon Valley in 5 minutes
Clear all Milla stages
Defeat an end boss with Milla's phantom blocks
Destroy a Chopper with a single Dragon Boost as Lilac
Clear Final Dreadnought 4 in 8 minutes
Clear all Carol stages
Defeat an end boss with Carol's Wild Claw
Dig into a treasure spot as Milla
Defeat an end boss with Carol's Wild Kick
Defeat an end boss while riding Carol's motorcycle
Let one of your teammates finish off Robopanther
Clear all Lilac stages
Clear Final Dreadnought 3 in 6 minutes
Clear Final Dreadnought 1 in 5 minutes
Destroy Prince Dail's shield before he finishes his monologue
Defeat an end boss with Lilac's Dragon Boost
Defeat an end boss with Milla's Super Shield Burst
Destroy the Eye Golem in Relic Maze with a push block
Clear Fortune Night in 8 minutes
Rest on the ledge during Lilac's fight with Spade
Bust some dance moves in Fortune Night
Trick the Bone Golem in Relic Maze into destroying itself
Clear Relic Maze as any character
Defeat an end boss with Lilac's Dragon Cyclone
Defeat an end boss with Lilac's Rising Slash
Skip the switch door in Dragon Valley as Lilac
Get a boulder to wrap around the screen