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