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