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