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