This paper studies the dynamics of the development of laser breakdown plasma in aqueous colloids of dysprosium nanoparticles by analyzing the time patterns of plasma images obtained using a high-speed streak camera. In addition, the distribution of plasma flashes in space and their luminosity were studied, and the amplitude of acoustic signals and the rate of generation of new chemical products were studied depending on the concentration of dysprosium nanoparticles in the colloid. Laser breakdown was initiated by pulsed radiation from a nanosecond Nd:YAG laser. It is shown that the size of the plasma flash, the speed of motion of the plasma–liquid interface, and the lifetime of the plasma flash decrease with an increasing concentration of nanoparticles in the colloid. In this case, the time delay between the beginning of the laser pulse and the moment the plasma flash reaches its maximum intensity increases with increasing concentrations of nanoparticles. Varying the laser fluence in the range from 67 J/cm2 to 134 J/cm2 does not lead to noticeable changes in these parameters, due to the transition of the breakdown plasma to the critical regime. For dysprosium nanoparticles during laser breakdown of colloids, a decrease in the yield of hydrogen peroxide and an increase in the rate of formation of hydroxyl radicals per water molecule, characteristic of nanoparticles of rare earth metals, are observed, which may be due to the participation of nanoparticles and hydrogen peroxide in reactions similar to the Fenton and Haber–Weiss reactions.