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