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