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