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