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