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