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