You can only do the accordion feature with javascript code. You would need to write it yourself or find someone to do it, and I doubt anybody is going to do it for free.
If you want to be able to see all subcategories of a category without reloading the page, CSS hover flyout menus can do it. There are at least two that work well, CSS Flyout Menu and Categories Dressing with its ch_categories option and a few CSS rules added from its support thread.