That part almost ended my run after a couple of failed attempts. And I mean BADLY failed.
My advice is to stock up on health (and heat, and health+heat) medicine. Don't forget to use the items around the rooms (chairs, computers, etc.) and attack enemies with them. They don't do a ton of damage usually, but can be good for hitting several guys at once.
Also, be sure to spend money to upgrade your abilities. The health increases in each fighting style apply to ALL fighting styles.