Here is the full list of all 28 Link The Cubes achievements.
Die in lava
Make a row of 3 cubes
Solve a very annoying ice level
Link 1000 times with a blue cube
Push a blue cube into the lava
Solve all fire levels
Link with a blue cube for the first time
Solve all ice levels
Solve 15 ice levels
Solve 10 levels without using UNDO
Solve 50 levels without using UNDO
Solve all levels without using UNDO
Link 100 times with a blue cube
Solve all levels
Use UNDO 500 times
Solve your first level
Solve 10 lava levels
Unlock your first door
Find the secret room
Leave all blue cubes behind
Save 10 blue cubes
Save 25 blue cubes
Save 50 blue cubes
Save 75 blue cubes
Save 100 blue cubes
Save 125 blue cubes
Save every blue cube
Slide a really long way in the hub world