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