Dung beetles impressively coordinate their six legs simultaneously to effectively roll large dung balls. They are also capable of rolling dung balls varying in the weight on different terrains. The mechanisms underlying how their motor commands are adapted to walk and simultaneously roll balls (multitasking behavior) under different conditions remain unknown. Therefore, this study unravels the mechanisms of how dung beetles roll dung balls and adapt their leg movements to stably roll balls over different terrains for multitasking robots. We synthesize a modular neural-based loco-manipulation control inspired by and based on ethological observations of the ball-rolling behavior of dung beetles. The proposed neural-based control contains various neural modules, including a central pattern generator (CPG) module, a pattern formation network (PFN) module, and a robot orientation control (ROC) module. The integrated neural control mechanisms can successfully control a dung beetle-like robot (ALPHA) with biomechanical feet to perform adaptive robust (multitasking) loco-manipulation (walking and ball-rolling) on various terrains (flat and uneven). It can also deal with different ball weights (2.0 and 4.6 kg) and ball types (soft and rigid). The control mechanisms can serve as guiding principles for solving complex sensory-motor coordination for multitasking robots. Furthermore, this study contributes to biological research by enhancing our scientific understanding of sensory-motor coordination for complex adaptive (multitasking) loco-manipulation behavior in animals.