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