This paper presents a nonlinear model predictive control (NMPC) toward versatile motion generation for the telescopic-wheeled-legged robot Tachyon 3, the unique hardware structure of which poses challenges in control and motion planning. We apply the full-centroidal NMPC formulation with dedicated constraints that can capture the accurate kinematics and dynamics of Tachyon 3. We have developed a control pipeline that includes an internal state integrator to apply NMPC to Tachyon 3, the actuators of which employ high-gain position-controllers. We conducted simulation and hardware experiments on the perceptive locomotion of Tachyon 3 over structured terrains and demonstrated that the proposed method can achieve smooth and dynamic motion generation under harsh physical and environmental constraints.