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