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