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