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