A 700 kHz histotripsy array is used to generate repeated cavitation events in agarose, gelatin, and polyacrylamide hydrogels. High-speed optical imaging, a broadband hydrophone, and the narrow-band receive elements of the histotripsy array are used to capture bubble dynamics and acoustic cavitation emissions. Bubble radii, lifespan, shockwave amplitudes are noted to be measured in close agreement between the different observation methods. These features also decrease with increasing hydrogel stiffness for all of the tested materials. However, the evolutions of these properties during the repeated irradiations vary significantly across the different material subjects. Bubble maximum radius initially increases, then plateaus, and finally decreases in agarose, but remains constant across exposures in gelatin and polyacrylamide. The bubble lifespan increases monotonically in agarose and gelatin but decreases in polyacrylamide. Collapse shockwave amplitudes were measured to have different-shaped evolutions between all three of the tested materials. Bubble maximum radii, lifespans, and collapse shockwave amplitudes were observed to express evolutions that are dependent on the structure and stiffness of the nucleation medium.