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