You need to updated the control template and especially TopLevelHeaderTemplateKey of RadMenuItem in order to achieve the desired approach. Inside it look for Border element which is below Grid named "PopupContentElement" and set Border Background color to transparent.
I've demonstrated the approach in the attached project.
I hope it helps.
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.