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