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.
Do hard time
Earn 26 Relics (gold or better)
Just "forget" it. Repeatedly.
Earn 99 Lives
Earn 27 Relics (gold or better)
Die.
Have your bazooka ready.
Avoid whatever he's flinging at you.
Shoot 5 of them in a single level.
Earn 30 Relics (gold or better)
Earn the Gems in the bonus levels
Discovered the Secret Exit in Dino Might!
Seek and destroy. Again.
Shoot the Imposter
Earn 42 Gems
Earn 10 Relics (gold or better)
Defeat 5 enemies with Coco's Savage Hurricane Spin
Earn 5 Relics
Defeat N. Cortex
Shoot a background UFO in Future Tense.
Defeat N. Gin
Earn 21 Gems
Discover a Gem Path after earning a Color Gem
Defeat N. Tropy
Discovered the Secret Exit in Road Crash
Discover a Death Route
Defeat Dingodile
Defeat Tiny Tiger
Discover a "?" Bonus Path
Don't feel guilty about jumping on him.
Unlocked the Secret Exit in Hangin' Out
Unlocked the Secret Exit in Unbearable
Discover the Secret Exit in Air Crash
Discover the Secret Exit in Diggin' It
Die as Crash.
Discover the Secret Exit in Bear Down
Defeat 5 enemies with Coco's Double Leg Drop
Defeat the Komodo Brothers
Fly, then die.
Defeat Ripper Roo
Seek and destroy
Earn 26 Gems
Earn the Key in Sunset Vista
Earn the Key in Jaws of Darkness
Earn 13 Gems
Defeat N. Brio
Defeat Pinstripe Potoroo
Miss a lot of boxes.
Defeat Koala Kong
Defeat 5 enemies with Coco's Spin
Spin away an Extra Life
Defeat Papu-Papu
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice