As the elevator and rudder can be used actively for control, in addition to the rotors, Coaxial High-speed Helicopters (CHHs) have the problems of control redundancy and changing control authority in the transition mode. This paper presents a robust-augmentation transitioning flight control design for a CHH under the adverse conditions of parametric uncertainties and external disturbances. First, based on control characteristic analysis, an Adaptive Filtered Nonlinear Dynamic Inversion (AFNDI) controller is proposed for the angular rate to handle the effect of unknown unstructured uncertainties and external turbulence. Theoretical analysis proves that the presented angular rate controller can guarantee steady-state and transient performance. Furthermore, the attitude angle and velocity controllers are also added. Then, an Incremental-based Nonlinear Prioritizing Control Allocation (INPCA) method is designed to take into account control surface transition and changing control authority, which efficiently distributes the required moments between coaxial rotors and aero-surfaces, and avoids the control reversal problem of the yaw channel. In the proposed control architecture, the low-pass filter is introduced to alleviate the adverse influence of time delay and measurement noise. Finally, the effectiveness of the proposed controller is demonstrated through nonlinear numerical simulations, and is compared with existing methods. Simulation results show that the proposed control law can improve both capabilities of disturbance rejection and fast response, and works satisfactorily for the CHH transitioning control characteristic.