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