Here is the full list of all 25 Crash Bandicoot 2: Cortex Strikes Back trophies - there are 7 bronze, 11 silver, 6 gold and 1 platinum.
Earn 42 Gems.
Earn 99 lives.
Earn 10 Relics (gold or better).
Earn 5 Relics.
Just "forget" it. Repeatedly.
Unlocked the Secret Exit in Diggin' It.
Fly, then die.
Defeat N. Cortex.
Earn 21 Gems.
Defeat N. Gin.
Die as Crash.
Unlocked the Secret Exit in Hangin' Out.
Defeat 5 enemies with Coco's Double Leg Drop.
Defeat Tiny Tiger.
Unlocked the Secret Exit in Unbearable.
Unlocked the Secret Exit in Air Crash.
Unlocked the Secret Exit in Bear Down.
Defeat the Komodo Brothers.
Discover a Death Route.
Don't feel guilty about jumping on him.
Defeat Ripper Roo.
Discover a Gem Path after earning a Color Gem.
Discover a "?" Bonus Path.
Collect all the Crash Bandicoot 2: Cortex Strikes Back trophies.
Earn 27 Relics (gold or better).