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