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