Robots for underwater exploration are typically comprised of rigid materials and driven by propellers or jet thrusters, which consume a significant amount of power. Large power consumption necessitates a sizeable battery, which limits the ability to design a small robot. Propellers and jet thrusters generate considerable noise and vibration, which is counterproductive when studying acoustic signals or studying timid species. Bioinspired soft robots provide an approach for underwater exploration in which the robots are comprised of compliant materials that can better adapt to uncertain environments and take advantage of design elements that have been optimized in nature. In previous work, we demonstrated that frameless DEAs could use fluid electrodes to apply a voltage to the film and that effective locomotion in an eel-inspired robot could be achieved without the need for a rigid frame. However, the robot required an off-board power supply and a non-trivial control signal to achieve propulsion. To develop an untethered soft swimming robot powered by DEAs, we drew inspiration from the jellyfish and attached a ring of frameless DEAs to an inextensible layer to generate a unimorph structure that curves toward the passive side to generate power stroke, and efficiently recovers the original configuration as the robot coasts. This swimming strategy simplified the control system and allowed us to develop a soft robot capable of untethered swimming at an average speed of 3.2 mm/s and a cost of transport of 35. This work demonstrates the feasibility of using DEAs with fluid electrodes for low power, silent operation in underwater environments.