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