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