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