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