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