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