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