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Mobile soft robots offer compelling applications in fields ranging from urban search and rescue to planetary exploration. A critical challenge of soft robotic control is that the nonlinear dynamics imposed by soft materials often result in complex behaviors that are counter-intuitive and hard to model or predict. As a consequence, most behaviors for mobile soft robots are discovered through empirical trial and error and hand-tuning. A second challenge is that soft materials are difficult to simulate with high fidelity - leading to a significant reality gap when trying to discover or optimize new behaviors. In this work we employ a Quality Diversity Algorithm running model-free on a physical soft tensegrity robot that autonomously generates a behavioral repertoire with no a priori knowledge of the robot's dynamics, and minimal human intervention. The resulting behavior repertoire displays a diversity of unique locomotive gaits useful for a variety of tasks. These results help provide a road map for increasing the behavioral capabilities of mobile soft robots through real-world automation.