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This work presents a soft robotic fish that achieves large-amplitude tail fin bending through a novel design where dielectric elastomer actuators (DEAs) are functionally integrated to form the body. The challenge of combining structure and actuation is addressed by utilizing the bending of fiber-reinforced DEAs to create three-dimensional, hollow shapes. This active skin is prestretched against a flexible spring steel spine, forming a negative stiffness biasing system that enables large, efficient displacements. An analytical model based on energy landscapes is developed to predict and optimize the system's bistable switching and is subsequently experimentally validated. The prototype demonstrates a peak-to-peak fin tip displacement of about 55 mm at a low nominal electrical field-strength of 60 V/ μm and achieves a forward swimming speed of 6 cm/s at an actuation frequency of 6 Hz. This research establishes a new approach for exploiting mechanical anisotropy to create a integrated, bio-mimetic soft robotic fish. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.