Brillouin microscopy is an emerging optical elastography technique capable of assessing mechanical properties of biological samples in a three-dimensional, all-optical and noncontact fashion. The typically weak Brillouin scattering signal can be substantially enhanced via a stimulated Brillouin scattering (SBS) process; however, current implementations require high pump powers, which prohibit applications to photosensitive or live imaging of biological samples. Here we present a pulsed SBS scheme that takes advantage of the nonlinearity of the pump-probe interaction. In particular, we show that the required pump laser power can be decreased ~20-fold without affecting the signal levels or spectral precision. We demonstrate the low phototoxicity and high specificity of our pulsed SBS approach by imaging, with subcellular detail, sensitive single cells, zebrafish larvae, mouse embryos and adult Caenorhabditis elegans. Furthermore, our method permits observing the mechanics of organoids and C. elegans embryos over time, opening up further possibilities for the field of mechanobiology.