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.
Defeat Tiny Tiger
Discover a "?" Bonus Path
Defeat N. Cortex
Discover a Gem Path after earning a Color Gem
Spin away an Extra Life
Defeat N. Brio
Earn the Key in Jaws of Darkness
Defeat Pinstripe Potoroo
Die as Crash.
Miss a lot of boxes.
Defeat Koala Kong
Earn the Key in Sunset Vista
Defeat Ripper Roo
Defeat Papu-Papu
Enter a Bonus Round after collecting 3 Character Tokens
In a single level, spin an enemy into another enemy twice
Earn 5 Relics
Die.
Earn 10 Relics (gold or better)
Earn 13 Gems
Earn 26 Gems
Earn 26 Relics (gold or better)
Defeat 5 enemies with Coco's Spin
Earn 99 Lives
Defeat the Komodo Brothers
Don't feel guilty about jumping on him.
Just "forget" it. Repeatedly.
Defeat N. Gin
Discover a Death Route
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 21 Gems
Earn 42 Gems
Earn 27 Relics (gold or better)
Defeat 5 enemies with Coco's Double Leg Drop
Defeat Dingodile
Have your bazooka ready.
Shoot the Imposter
Shoot 5 of them in a single level.
Defeat N. Tropy
Discovered the Secret Exit in Road Crash
Discovered the Secret Exit in Dino Might!
Earn the Gems in the bonus levels
Avoid whatever he's flinging at you.
Earn 30 Relics (gold or better)
Defeat 5 enemies with Coco's Savage Hurricane Spin
Seek and destroy
Do hard time
Seek and destroy. Again.
Shoot a background UFO in Future Tense.