Oscillations are widely found in living organisms to generate propulsion-based locomotion often driven by constant ambient conditions, such as phototactic movements. Such environment-powered and environment-directed locomotions may advance fully autonomous remotely steered robots. However, most man-made oscillations require nonconstant energy input and cannot perform environment-dictated movement. Here, we report a self-sustained soft oscillator that exhibits perpetual and untethered locomotion as a phototactic soft swimming robot, remotely fueled and steered by constant visible light. This particular out-of-equilibrium actuation arises from a self-shadowing-enabled negative feedback loop inherent in the dynamic light-material interactions, promoted by the fast and substantial volume change of the photoresponsive hydrogel. Our analytical model and governing equation unveil the oscillation mechanism and design principle with key parameters identified to tune the dynamics. On this autonomous oscillator platform, we establish a broadly applicable principle for converting a continuous input into a discontinuous output. The modular design can be customized to accommodate various forms of input energy and to generate diverse oscillatory behaviors. The hydrogel oscillator showcases agile life-like omnidirectional motion in the entire three-dimensional space with near-infinite degrees of freedom. The large force generated by the powerful and long-lasting oscillation can sufficiently overcome water damping and effectively self-propel away from a light source. Such a hydrogel oscillator-based all-soft swimming robot, named OsciBot, demonstrated high-speed and controllable phototactic locomotion. This autonomous robot is battery free, deployable, scalable, and integratable. Artificial phototaxis opens broad opportunities in maneuverable marine automated systems, miniaturized transportation, and solar sails.