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