Qualifications
A rolodex. It's everything. Whom you know matters more than anything else. And more importantly, who will write you a check to go looking for employees on their behalf.
An MBA is nice, mainly for the shmooze factor; business school is a great way to meet lots and lots of people inside of a given industry. Some headhunters dropped out of law school, or maybe even finished and worked in the laugh (read: law) field for a while. There's always demand for good lawyers who can chase ambulances, litigate global patent suits, or attract corporate paperwork dollars.