To combat a mildew problem like you describe, you're going to have to replace the affected area with new wallboard. That's really the only thing that will prevent the mold from reappearing. Georgia-Pacific has a brand new product that can help make sure you don't have a reoccurance. DensArmor Interior Guard wall panels have a gypsum core like traditional wallboard but instead of paper, the product has a fiberglass mat on the back that prevents moisture intrusion. In addition, because the mat is inorganic, it resists the growth of mold.
As far as how to replace the board, G-P has a booklet on line that describes wallboard installation. FYI: DensArmor installs just like regular wallboard! The booklet is called The Wallworks Guide. You can find it at www.gp.com/gypsum in the DIY section of the site.