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