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