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Controlling agile and complex air-vehicle maneuvers requires knowledge of the full flight envelope and dominant modes of motion. This paper presents a comprehensive approach for determining the full flight envelope and trim map of minimally actuated flapping-wing micro aerial vehicles that are capable of a broad range of coupled longitudinal-lateral-directional aerobatic maneuvers. By this approach, a representative set of realizable set points and trim conditions can be determined from the flight dynamic model, including asymmetric and unstable maneuvers. Data-driven dynamic mode decomposition is used to identify and analyze the dominant modes of motion both in simulations and physical experiments involving the RoboBee. The dominant eigenplanes and stability characteristics of this flapping-wing robot are successfully validated experimentally for both stable and unstable asymmetric full-envelope maneuvers, including rapidly uncontrolled tumbling.