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