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