Here is the full list of all 16 Prelogate achievements.
Do over 9000 total logic ticks in your solutions
Complete the game
Find clean solution for every level in the game
Complete IX.6 with finite, total laser length exceeding 128 units
Make logic circuit loop endlessly
Use 512 devices in your solutions
Complete VII.3 with finite, total laser length exceeding 270 units
Complete chapter VI using less than 64 devices
Solve VI.5 using exactly ten devices
Solve V.6 with less than 240 total logic ticks
Complete fifth chapter
Find clean solution to III.4 without using Mixer
Don't cross the beams in III.3
Discover at least one of them
Solve II.4 using exactly five devices
Complete tutorial chapter