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