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