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