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