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 27 Relics (gold or better)
Do hard time
Seek and destroy
Shoot a background UFO in Future Tense.
Die.
Shoot 5 of them in a single level.
Avoid whatever he's flinging at you.
Seek and destroy. Again.
Shoot the Imposter
Earn 30 Relics (gold or better)
Earn 42 Gems
Earn 99 Lives
Have your bazooka ready.
Earn the Gems in the bonus levels
Discovered the Secret Exit in Dino Might!
Earn 26 Relics (gold or better)
Earn 10 Relics (gold or better)
Defeat N. Cortex
Defeat N. Gin
Discover a Gem Path after earning a Color Gem
Earn 21 Gems
Earn 5 Relics
Defeat 5 enemies with Coco's Savage Hurricane Spin
Defeat N. Tropy
Discover a Death Route
Discovered the Secret Exit in Road Crash
Defeat Dingodile
Defeat Tiny Tiger
Discover a "?" Bonus Path
Fly, then die.
Discover the Secret Exit in Diggin' It
Die as Crash.
Earn 26 Gems
Unlocked the Secret Exit in Hangin' Out
Defeat 5 enemies with Coco's Double Leg Drop
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
Just "forget" it. Repeatedly.
Defeat 5 enemies with Coco's Spin
Defeat N. Brio
Earn the Key in Jaws of Darkness
Earn 13 Gems
Defeat Pinstripe Potoroo
Miss a lot of boxes.
Defeat Koala Kong
Earn the Key in Sunset Vista
Spin away an Extra Life
Defeat Papu-Papu
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice