No straight and narrow academic path leads the way to being an HR director. At minimum, as for most professional jobs in the 21st century, you need that bachelor's degree in… something. Well, maybe not just anything -- you would probably have to supplement your courses in painting and basket-weaving and modern dance with heftier fare such as statistics, English, economics and behavioral sciences.
If you have a hankering for additional academic credentials, you can get a master's degree in business administration, human resources management, industrial relations or, even better, a law degree (with special emphasis on labor law). As a graduate student, you'll delve further into areas like talent management strategy (e.g., what makes workplace tick and how to manage these ticks) and organizational behavior (why people do what they do and how to manage what they do).
But it takes more than book-learning to make it as an HR director. Each company has its own customs, rules and regulations about life in the workplace, and it's just as important to master the protocols as it is to have a bunch of sheepskins.
And most important of all, an HR director should have the equivalent of a PhD in people skills. HR honchos will be maneuvering around ego-mad superiors and subordinates, turf-protecting department heads, disgruntled employee/employer factions, palace revolts, boardroom coups, natural disasters, safety violations, workplace harassment. If you like to try to fix things, you'll love being an HR director.