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