How to achieve MuchoMenu Multilingual functionality?
Looking their module code, it appears as though they did not encapsulate many of their strings in the t() function. Therefore it's not exposed to Drupal's string translation functions. Unless you want to undertake the task of fixing it then, unfortunately, it's not available. 

You could also lodge a bug in their issue queue and maybe that will motivate some discussion on their end. 

Regardless, as long as mucho menu uses Drupal's native menu handler, it SHOULD still use the same functions for translation for links. Assuming you set up the menu to be translatable the links should be exposed as any other menu in Drupal.