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