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