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