Untethered microrobots offer a great promise for localized targeted therapy in hard-to-access spaces in our body. Despite recent advancements, most microrobot propulsion capabilities have been limited to homogenous Newtonian fluids. However, the biological fluids present in our body are heterogeneous and have shear rate–dependent rheological properties, which limit the propulsion of microrobots using conventional designs and actuation methods. We propose an acoustically powered microrobotic system, consisting of a three-dimensionally printed 30-micrometer-diameter hollow body with an oscillatory microbubble, to generate high shear rate fluidic flow for propulsion in complex biofluids. The acoustically induced microstreaming flow leads to distinct surface-slipping and puller-type propulsion modes in Newtonian and non-Newtonian fluids, respectively. We demonstrate efficient propulsion of the microrobots in diverse biological fluids, including in vitro navigation through mucus layers on biologically relevant three-dimensional surfaces. The microrobot design and high shear rate propulsion mechanism discussed herein could open new possibilities to deploy microrobots in complex biofluids toward minimally invasive targeted therapy.