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