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In this paper, a robust hybrid backstepping and sliding mode control is designed for lateral-directional control of a highly maneuverable aircraft. A systematic approach is implemented in tracking the reference trajectory of a high-fidelity aircraft model, which inculcates non-linear coupled dynamics. A smooth switching function to eliminate the chattering phenomenon is used in the sliding surface and integrated into the backstepping architecture, which guarantees asymptotic stability of the state trajectories. Separate controllers are designed for longitudinal dynamics to address the system in the strict-feedback form, which is an essence of the backstepping methodology. For backstepping control, angular rates are utilized as virtual control inputs in the subsystems considered. Stability analysis is carried out meticulously in the sense of Lyapunov, which guarantees closed-loop system stability. The performance of the considered controllers in the paper is evaluated with the minimum gains by infusing random uncertainties in the aerodynamic model and inertial parameters. Various real-time flight scenarios pertaining to lateral-directional dynamics with and without side-wind are simulated and discussed.