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