Here is the full list of all 53 Q.U.B.E: Director's Cut achievements.
Complete Q.U.B.E.
Winning a race for the first time
Complete Sector 7
Complete the final physics puzzle
Complete the second ball puzzle in Sector 7
Complete Sector 6
Complete the hardest puzzle in the game
Make 1,000 Moves
Complete Sector 5
Complete the series of magnet puzzles in Sector 5
Complete Sector 4
Complete the hidden puzzle in Sector 4
Complete Sector 3
Complete Sector 2
Complete Sector 1
Complete the tutorial
Find a picture of the developers
Find the hidden area in Sector 5
Complete the hidden beta puzzle
Attempt to extrude the developers
Push the ball in the hidden area to the end
Don't touch the floor
Jump on certain cubes in sequence
Get 3 gold medals in every level
Make 1,000 moves in Time Trial mode
Travel 10,000 metres
Travel 100,000 metres
Collect 250 pickups
Collect 1,000 pickups
Collect 10,000 pickups
Play the game 100 times
Play the game 500 times
Beat the Developer's Time in SPEED WAY
Beat the Developer's Time in PLANS FOR FANS
Beat the Developer's Time in ROTATION STATION
Beat the Developer's Time in A NEW HOPE
Beat the Developer's Time in NEON NIGHTMARE
Beat the Developer's Time in LOST
Beat the Developer's Time in TIME BOMB
Beat the Developer's Time in RUIN RUSH
Beat the Developer's Time in HOVER HEADWAY
Beat the Developer's Time in SPACE RACE
Complete SPEED WAY in the least amount of moves
Complete PLANS FOR FANS in the least amount of moves
Complete ROTATION STATION in the least amount of moves
Complete A NEW HOPE in the least amount of moves
Complete NEON NIGHTMARE in the least amount of moves
Complete LOST in the least amount of moves
Complete TIME BOMB in the least amount of moves
Complete RUIN RUSH in the least amount of moves
Complete HOVER HEADWAY in the least amount of moves
Complete SPACE RACE in the least amount of moves
Complete the hidden puzzle in Sector 6