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