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