I am using Firefox 13 in Ubuntu 12.04.
How can I access the Firefox 13 menu in Unity's global menu bar? I am using to the whole Firefox menu appearing when I hold down the Alt key.
How did you install Firefox? I'm using Firefox 13 on Ubuntu 12.04 and the menu bar appears on Unity (this is called "global menu bar"). This is done with an addon called firefox-globalmenu. If you somehow installed Firefox from a non-ubuntu package, that may be the problem.
You can try opening a terminal and typing
this will either install the package or tell you that it's already installed.