To get this achievement, you must start a new game and play all the way to the Monkey Shrine without dying. This is found shortly after the Biohunter boss fight. I can confirm you can quit the game if you are near death and restart without voiding the achievement. The hardest part is dodging enemies next to an instant death spot. Be patient and play safe. Clear out all enemies you are able to in safe locations, and if you get to two health bars I would suggest exiting to the main menu and retrying from your last checkpoint. It took me a good amount of attempts, but if you can clear out the enemies away from instant death spots, it's not too bad.
Good luck!