Here is the full list of all 22 POLYBIUS achievements.
Achieve ultimate transcendence (by getting every achievement)
Get every fried egg in Level 6
Complete any level
Get to level 10
Get maximum shields in Pure Mode
Complete at least 1 level in all 3 game modes
Get to level 13 in YOLO Mode
Finish the game in Normal Mode
Get to level 30 in Pure Mode
Finish a level under full Red Pill boost
Finish a level without shooting
Complete a level without losing a shield
Do 3 consecutive levels without losing a shield
Get 10 'Perfect' shooting ratings during one game
Use 10 lift gates without landing
Fly for 50 seconds or longer
Become a bull
Hands off controls for 30 seconds
Do 5 consecutive levels without losing a shield
Do 10 consecutive 1000+ point slalom gates
Use 5 consecutive Boost pills without any collisions
Tauroctony