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