Here is the full list of all 38 Quell Reflect achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Complete every level in perfect moves
Complete every level
Collect every jewel
Collect 200 pearls
Complete the 1974 shelf
Complete a level requiring 4 drops
Complete the 1972 shelf
Spiked 15 times
Collect 150 pearls
Close 50 gates
Complete the 1970 shelf
Complete 40 levels perfectly
Complete the 1967 shelf
Poison 2 drops in order to continue
Collect 100 pearls
Break 15 gold blocks
Break 3 gold blocks in one level
Complete a level requiring 3 drops
Get stuck in a loop 5 times
Complete the 1964 shelf
Complete 20 levels perfectly
Push 10 spikes
Merge drops 3 times
Collect 50 pearls
Spike a poisoned drop
Complete the 1962 tutorial shelf
Complete a shelf in perfect moves
Complete 10 levels perfectly
Spiked 5 times
Push 4 sets of blocks together
Sacrifice a drop in order to continue
Collect 25 pearls
Complete a level requiring 2 drops
Use the ring 10 times
Complete a stage in perfect moves
Complete 3 levels perfectly
Retry a level 10 times
Complete a level in under 6 seconds