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