This paper addresses the issue of robust tracking control of Coaxial Octorotor Unmanned Aerial Vehicles (COUAVs). First, a novel Multiple-Input-Multiple-Output (MIMO) super-twisting Sliding Mode Controller (SMC) is proposed for a wide range of systems, in which uncertainties and disturbances are estimated through a Multilayer Perceptron Neural Network (MLPNN). Lyapunov stability theory is used to guarantee the stability of the closed loop system. The real-time update laws for the MLPNN weights are formulated within the stability analysis. The effectiveness of the proposed controller is demonstrated through its application to control uncertain COUAVs in the presence of disturbances. A control structure employing an inner-outer loop framework is adopted to handle the underactuated COUAV dynamics. Simulations involving a commercial heavy-lift COUAV are presented, illustrating the robustness and efficacy of the proposed method.