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