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