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