Here is the full list of all 22 Polybius trophies - there are 6 bronze, 8 silver, 7 gold and 1 platinum.
Finish a level without shooting
Get every fried egg in level 6
Try all three game modes
Complete a level without losing a shield
Use 5 consecutive Boost pills with no collisions
Hands off the controls for 30 seconds
Get to level 10
Finish a level under full boost
Complete any level
Achieve ultimate transcendence
Get maximum shields in Pure mode
Get to level 13 in YOLO mode
Finish the game in Normal mode
Get to level 30 in Pure Mode
Do three consecutive levels without losing a shield
Get 10 'Perfect' accuracies in one game
Use 10 lift gates without landing
Fly for 50 seconds or longer
Become a bull
Do 5 consecutive levels without losing a shield
Do 10 consecutive 1000+ point slalom gates
Kill 1000 cattle during a game