After a couple dozen tries where I got to 15k or so before being hit I managed to get to 45k before my first hit, way more than needed for the badge. Apparently I just really needed to get into the zone.
I enjoy the challenge of trying to solve a puzzle while also frantically running away from zombies. I only wish there was a pause button. There's nothing more frustrating than being at 400 points and being called away from the computer.