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