(not a complete answer, but too much for a comment)
The main characteristic of a "mega menu" is that the contents of the menu are not limited to a simple list or tree of menu links. In your own example you have links with descriptions / subtitles, you have a picture, you have multiple columns that probably have nothing to do with a menu tree structure.
This is why you should use tools other than menu links system, for the contents of each megamenu box.
The first step is to forget you are creating a menu, and instead imagine you would be creating custom pages or blocks. How you create these, is a question for itself.
I have heard of someone who used nodes (possibly with pragraphs module), where every megamenu page is a node.
Another option would be to do something with panels.
The next question is how to anchor the megamenu contents to the actual menu items.
The person who used nodes for the megamenu pages (if I remember correctly) used a field where people specify the menu link path. Then when displaying the menu, the contents from the matching node are inserted as submenu.
You could also completely give up on the links being menu links, and instead just display node titles as toplevel items (sorted by whichever criterion), and then the rendered node as "submenus". This could be done with views, if you use a ul/li list as the style plugin (with custom classes) and a special view mode + layout for each item with its megamenu page. The special html you need would be in the custom layout.
Special attention should be given to multiple language versions, and possibly access checks for links. Maybe you use different paths in different languages?
This still requires some creativity in putting everything together.
But the main idea should be to look for solutions outside the menu links system.
EDIT:
I should add: You may want to think about doing something with ajax, to let the contents of the pages load after the main page contents. If I remember correctly, the person I talked to did this somehow, I just don't remember how exactly.
Credits to https://twitter.com/rachel_norfolk