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 26 Relics (gold or better)
Do hard time
Earn 10 Relics (gold or better)
Earn 5 Relics
Seek and destroy
Earn 26 Gems
Earn 13 Gems
Earn the Key in Jaws of Darkness
Earn 99 Lives
Defeat 5 enemies with Coco's Spin
Earn 27 Relics (gold or better)
Just "forget" it. Repeatedly.
Defeat 5 enemies with Coco's Double Leg Drop
Die.
Avoid whatever he's flinging at you.
Shoot 5 of them in a single level.
Have your bazooka ready.
Shoot the Imposter
Earn 42 Gems
Earn 30 Relics (gold or better)
Defeat 5 enemies with Coco's Savage Hurricane Spin
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
Seek and destroy. Again.
Defeat N. Cortex
Discover a Gem Path after earning a Color Gem
Earn 21 Gems
Defeat N. Gin
Defeat N. Tropy
Discover a Death Route
Defeat Dingodile
Defeat Tiny Tiger
Discover a "?" Bonus Path
Discover the Secret Exit in Diggin' It
Unlocked the Secret Exit in Hangin' Out
Die as Crash.
Fly, then die.
Unlocked the Secret Exit in Unbearable
Discover the Secret Exit in Air Crash
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
Miss a lot of boxes.
Defeat Pinstripe Potoroo
Defeat Koala Kong
Earn the Key in Sunset Vista
Defeat Papu-Papu
Spin away an Extra Life
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice