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