First, that webpart uses a standard unordered list < ul > < li > structure so you should be able to find some CSS and jQuery examples on Google that will get you in the right direction.

Second, depending on your design the menu is bound to change so we're not going to be able to help much if we don't see a design or know what you're looking for.

Third, there are a few different ways you can attemtp this, for instance you could have the CSSList Menu webpart as your main navigation and use a Repeater for your mobile/tablet navigation. Do you know if you're going to use straight media queries or utilize some or all of the features Kentico has to offer?