Here is the full list of all 25 Puzzle Dimension achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Score over 500 in a puzzle
Get a multiplier of 8
Complete all puzzles in the cluster Broken Ice
Score over 250 in a puzzle
Complete five puzzles
Score over 100 in a puzzle
Complete the tutorial
Complete all puzzles in the cluster Jump in the Fire
Complete all puzzles in the cluster Toggled Blocks
Complete all puzzles in the cluster Shifting Sands
Complete all puzzles in the cluster Hidden Blocks
Complete all puzzles in the cluster Bends
Complete all puzzles in the cluster Flat
Complete all puzzles in the cluster Revisited
Complete all puzzles in the cluster Mix
Complete all puzzles in the cluster The End
Unpixelate all blocks in the game
Get a multiplier of 16
Get a multiplier of 32
Score over 190 on the first puzzle in Broken Ice
Score over 1,000 in a puzzle
Solve every puzzle in the game
Get a total score of 10,000
Get a total score of 25,000
Get a total score of 50,000