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