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 the Gems in the bonus levels
Discovered the Secret Exit in Dino Might!
Shoot 5 of them in a single level.
Earn 42 Gems
Seek and destroy. Again.
Discover a Death Route
Earn 99 Lives
Have your bazooka ready.
Earn 10 Relics (gold or better)
Earn 21 Gems
Discover a Gem Path after earning a Color Gem
Shoot a background UFO in Future Tense.
Defeat N. Cortex
Defeat N. Gin
Defeat 5 enemies with Coco's Savage Hurricane Spin
Avoid whatever he's flinging at you.
Die.
Defeat N. Tropy
Discovered the Secret Exit in Road Crash
Earn 5 Relics
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
Discover the Secret Exit in Air Crash
Defeat 5 enemies with Coco's Double Leg Drop
Die as Crash.
Unlocked the Secret Exit in Hangin' Out
Unlocked the Secret Exit in Unbearable
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 26 Gems
Earn 26 Relics (gold or better)
Defeat N. Brio
Earn the Key in Jaws of Darkness
Defeat Pinstripe Potoroo
Earn 13 Gems
Defeat Koala Kong
Earn the Key in Sunset Vista
Do hard time
Seek and destroy
Spin away an Extra Life
Defeat 5 enemies with Coco's Spin
Defeat Papu-Papu
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