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