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