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