Here is the full list of all 16 Great Permutator achievements.
Collide 3 boxes
Complete a level in at least 300 cycles
Complete a level covering all 121 tiles
Solve any 3 levels
Solve all 25 levels from the first page
Solve all 50 main levels
Solve all 50 main levels with A+ grade
Complete Multi Teleport Pack
Complete Randomizer Pack
Complete Black Box Pack
Solve all bonus levels with A+ grade
Complete a level placing 3 blocks in one vertical row
Complete a level using not all action blocks
Move 5 boxes to output conveyors simultaneously
Destroy all boxes without completing the level
Get 50 boxes on the field at the same time