Navigating and exploring the surfaces of bodies of water allow swimming robots to perform a range of measurements while efficiently communicating and harvesting energy from the Sun. Such environments are often highly unstructured and cluttered with plant matter, animals, and debris, which require robots to move swiftly. We report a fast (5.1 centimeters per second translation and 195 degrees per second rotation), centimeter-scale swimming robot with high maneuverability and autonomous untethered operation. Locomotion is enabled by a pair of soft, millimeter-thin, undulating pectoral fins, in which traveling waves are electrically excited to generate propulsion. The actuators, robot design, and power supply are codesigned to enable high-performance locomotion in a scaled-down system. A single soft electrohydraulic actuator per side generates the traveling wave. A compact and lightweight power supply enables untethered operation, made possible by decreasing the operating voltage of the electrohydraulic actuators to below 500 volts and their power consumption to 35 milliwatts. By an experimental study and by modeling, we determined optimum dimensions and operating conditions across designs and size scales. The robots navigate through narrow spaces and through grassy plants and push objects weighing more than 16 times their body weight. Such robots can allow exploration of complex environments as well as continuous measurement of plant and water parameters for aquafarming.