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