Shock wave ultrasound therapy techniques, increasingly used for non-invasive surgery, require extremely high pressure amplitudes in precise focal spots, and large high-power transducers arranged on a spherical shell are usually used to achieve that. This solution allows limited steering of the beam around the geometrical focus of the device at the cost of a large number of transducer elements, and the treatment of large and moving organs like the heart is challenging or impossible. This paper validates numerically and experimentally the possibility of using a time reversal cavity (TRC) for the same purpose. A 128-element, 1 MHz power transducer combined with different multiple scattering media in a TRC was used. We were able to focus high-power ultrasound pulses over a large volume in a controlled manner, with a limited number of transducer elements. We reached sufficiently high pressure amplitudes to erode an Ultracal® target over a 10 cm2 area.