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