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