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