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