When a single-axis parallel hybrid electric vehicle (HEV) equipped with a multi-speed AMT gearbox is in its shifting process, the superposition of dynamic characteristics of multiple power sources and the intervention and withdrawal of AMT transmissions can easily cause significant vehicle longitudinal jerk. To achieve rapid and smooth output changes during the shifting process, this paper proposes an integrated multi-stage robust shifting control method for a single-axis parallel hybrid electric vehicles with a multi-speed AMT gearbox. First, models of key driveline components are constructed, and the shifting process is divided into five stages to provide a clear description of the control problem. Subsequently, we reproduce an integrated multistage robust control method to achieve favorable switching performance and control robustness under external disturbances. We propose a data-driven model predictive control strategy based on additional constraints in the torque unloading and recovery phases. Simultaneously, we present a joint control algorithm that integrates the optimal control and disturbance suppression in the speed synchronization phase. In addition, we develop a sliding mode auto-disturbance rejection control algorithm to achieve accurate position tracking of the shift actuator in the pickup and engage phases. Finally, simulations and bench tests are carried out to verify the effectiveness of the robust control method under different driving conditions. The results demonstrate that the proposed control method can not only coordinate the torque across different power sources and clutch while minimizing vehicle longitudinal jerk, shift time, and friction work, but also provides apparent robustness to model uncertainties and external disturbance. Therefore, the proposed method may offer a theoretical reference for the actual vehicle controller during shifting.