This paper addresses the energy dispatch problem for multi-stakeholder multiple microgrids (MMGs) under uncertainty while considering independent market operators (IMOs) based energy trading forms. Firstly, a collaborative hierarchical dispatch framework is proposed to adapt to decentralized multiple stakeholders and coordinate energy trading between IMOs and microgrids (MGs). And then this framework is further decomposed into different independent optimization problems for stakeholders based on an analytical target cascading (ATC) algorithm, in which Lagrangian penalty terms are introduced to ensure consistency in energy trading. In these optimization problems, energy trading and production of an individual MG is formulated as a two-stage adaptive robust optimization model to hedge against uncertainties from random renewable energy sources and loads. Moreover, in order to realize parallel computing for all independent optimization problems, a diagonal quadratic approximation method is applied to linearize quadratic terms. We integrate the ATC algorithm with a column-and-constraint generation algorithm to derive robust energy dispatch schemes in parallel. Finally, simulations on different cases are conducted to testify the rationality and validity of the proposed robust distributed energy dispatch approach. The results show that the hierarchical energy dispatch framework with IMOs has advantages over that without IMOs. Moreover, the proposed approach can reduce the impacts of uncertainties on distributed decision making of multiple stakeholder and enhance the computational efficiency.