This article is devoted to addressing the cluster formation-containment tracking problem of networked robotic systems (NRSs) with unknown model uncertainties and disturbances under directed graphs. A novel hierarchical prescribed-time extended state observer (ESO) based control algorithm is developed such that all the robotic systems are divided into multiple subgroups. For any subgroup, the master nodes form the different desired formation shapes at specific time points and the center of the shape follows the trajectory of the related target. Moreover, the follower nodes converge into the corresponding formation shapes. In the estimator loop, a cluster time-varying formation-containment tracking (TVFCT) algorithm is designed by employing a time-varying function such that the cluster formation shape can be guaranteed. In the local control loop, an extended state observer is employed to estimate the total disturbances (model uncertainties and disturbances) within a prescribed time. Then, a local control algorithm is designed by incorporating a sliding mode strategy such that the cluster TVFCT problem of the NRSs can be addressed within a prescribed time, where the convergence time can be set freely by choosing a tunable constant irrespective of the initial conditions. By constructing the Lyapunov function, several sufficient criteria for stability analysis are derived. Finally, some simulation examples are proposed to demonstrate the efficiency of the main results.