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