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