I have held the title of Director, Human Resources for six years. I also frequently recruit for human resources professionals. First you have to decide if you want to be a generalist or a specialist in HR. Both roles can lead to a director level position. If your focus is a generalist HR Director, you don't need a particular educational background. To get started you may want to work for a small organization where you get to do a lot of differnt things in HR like training, recruiting, employee relations, safety, etc. This way you get exposure to the various roles in HR. Do that for a few years and then seek a promotion within the company or somewhere else. Some large organizations will hire entry level folks and rotate them through the different HR functions which in essence is the same thing.
If you want to specialize like in compensation, then you need to have a background in math and analytics to get a junior role. Then you need to prove yourself for more challenging jobs to get ahead.