Here is the full list of all 77 Crash Bandicoot N. Sane Trilogy achievements worth 3,000 gamerscore.
Collect all the Crash Bandicoot 3: Warped Achievements
Earn 99 Lives.
Shoot a background UFO in Future Tense.
Die.
Avoid whatever he's flinging at you.
Shoot 5 of them in a single level.
Have your bazooka ready.
Shoot the imposter.
Earn 30 Relics (gold or better).
Earn the Gems in the bonus levels.
Discover the Secret Exit in Road Crash.
Discover the Secret Exit in Dino Might!
Seek and destroy. Again.
Earn 42 Gems.
Earn 10 Relics (gold or better).
Earn 5 Relics.
Discover a Gem Path after earning a Color Gem.
Defeat 5 enemies with Coco's Savage Hurricane Spin.
Defeat N. Cortex.
Earn 21 Gems.
Defeat N. Gin.
Defeat N. Tropy.
Discover a Death Route.
Defeat Dingodile.
Defeat Tiny Tiger.
Discover a "?" Bonus Path.
Collect all the Crash Bandicoot 2: Cortex Strikes Back Achievements
Just "forget" it. Repeatedly.
Earn 27 Relics (gold or better).
Discover the Secret Exit in Diggin' It.
Defeat 5 enemies with Coco's Double Leg Drop.
Don't feel guilty about jumping on him.
Fly, then die.
Discover the Secret Exit in Air Crash.
Die as Crash.
Discover the Secret Exit in Hangin' Out.
Discover the Secret Exit in Unbearable.
Discover the Secret Exit in Bear Down.
Defeat the Komodo Brothers.
Defeat Ripper Roo.
Collect all the Crash Bandicoot Achievements
Earn 26 Relics (gold or better).
Do hard time.
Earn 26 Gems.
Seek and destroy.
Earn the Key in Jaws of Darkness.
Earn 13 Gems.
Defeat 5 enemies with Coco's Spin.
Defeat N. Brio.
Defeat Pinstripe Potoroo.
Miss a lot of boxes.
Defeat Koala Kong.
Earn the Key in Sunset Vista.
Defeat Papu-Papu.
Enter a Bonus Round after collecting 3 Character Tokens.
In a single level, spin an enemy into another enemy twice.
Spin away an Extra Life.