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