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