Here is the full list of all 74 Crash Bandicoot N. Sane Trilogy achievements. It takes around 40-50 hours to unlock all of the achievements on Windows.
Die.
Don't feel guilty about jumping on him.
Just "forget" it. Repeatedly.
Earn 99 Lives
Avoid whatever he's flinging at you.
Have your bazooka ready.
Shoot 5 of them in a single level.
Seek and destroy. Again.
Shoot the Imposter
Shoot a background UFO in Future Tense.
Earn 30 Relics (gold or better)
Earn the Gems in the bonus levels
Discovered the Secret Exit in Dino Might!
Discovered the Secret Exit in Road Crash
Earn 42 Gems
Defeat 5 enemies with Coco's Savage Hurricane Spin
Discover a Gem Path after earning a Color Gem
Earn 10 Relics (gold or better)
Defeat N. Cortex
Earn 21 Gems
Defeat N. Gin
Earn 5 Relics
Defeat N. Tropy
Discover a Death Route
Defeat Dingodile
Defeat Tiny Tiger
Discover a "?" Bonus Path
Defeat 5 enemies with Coco's Double Leg Drop
Earn 27 Relics (gold or better)
Discover the Secret Exit in Diggin' It
Die as Crash.
Unlocked the Secret Exit in Hangin' Out
Unlocked the Secret Exit in Unbearable
Discover the Secret Exit in Bear Down
Defeat the Komodo Brothers
Fly, then die.
Discover the Secret Exit in Air Crash
Defeat Ripper Roo
Do hard time
Earn 26 Relics (gold or better)
Earn 26 Gems
Defeat N. Brio
Earn 13 Gems
Earn the Key in Jaws of Darkness
Defeat Pinstripe Potoroo
Miss a lot of boxes.
Defeat Koala Kong
Earn the Key in Sunset Vista
Spin away an Extra Life
Defeat 5 enemies with Coco's Spin
Seek and destroy
Defeat Papu-Papu
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice