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