The site you reference is using Categories Dressing, so your goal is feasible.
The first thing to do if you want the flyout subcategories feature is to install the chcategories option as the readme instructs.
Then apply the CSS rules from post 1608 in this thread.

You have made non-linked headings for each top category; is that what you want? Or do you want the top cats to look like those headings?