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