Fetch categories to TinyMce menu

Can anyone point me in the right direction?

I’ve got custom TinyMce menu added to the editor. I’m fine inserting shortcodes without arguments, but in this case I need to fetch the names of custom post categories to a dialog in TinyMce and allow the user to select one/multiple categories from there. Selection will then be passed as arguments to my shortcode.
So I need to dynamically generate that list in javascript – as far as I understand.