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