Here is the full list of all 35 Quell achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Get stuck in a loop 5 times
Play for 1 hour
Complete the 1939 shelf
Collect 100 pearls
Complete 20 levels perfectly
Take over 10 minutes to complete a level
Play for 30 minutes
Be spiked 10 times
Die on a first move
Complete the 1937 shelf
Push 10 blocks
Play for 10 minutes
Collect 50 pearls
Complete 10 levels perfectly
Complete the 1928 shelf
Push 2 sets of blocks together
Take twice as many moves as necessary
Use the ring 5 times
Be spiked 3 times
Complete a stage in perfect moves
Collect 25 pearls
Complete 3 levels perfectly
Complete a level in under 5 seconds
Collect 150 pearls
Collect 200 pearls
Complete the 1941 shelf
Complete the 1943 shelf
Complete the 1945 shelf
Complete every Quell level
Complete 40 levels perfectly
Complete a shelf in perfect moves
Complete every Quell level in perfect moves
Spiked 20 times
Retry a level 20 times
Collect every jewel