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