Herein we report a new design for acoustic nanoswimmers, making use of a nanoshell geometry that was synthesized using a sphere template process. Such shell-shaped nanomotors display highly efficient acoustic propulsion on the nanoscale by converting energy from the ambient acoustic field into motion. The propulsion mechanism of the nanoshell motors relies on acoustic streaming stress over the asymmetric surface to produce the driving force for motion. The shell-shaped nanomotors offer a high surface area to volume ratio, allow for efficient scalability and provide higher cargo towing capacity (in comparison to acoustically propelled nanowires). Furthermore, a detailed study of the parameters relevant to propulsion performance, including the material density, size and shape of the motors, reveals that the nanoshell motors exhibit a different propulsion behavior from that predicted by recent theoretical and experimental models for acoustically propelled nanomotors. Such findings indicate that further studies are needed to predict the behavior of acoustic nanomotors with different geometry designs. Practical applications of the new nanoshell motors, including "on-the-move" capture and the transport of multiple cargoes and internalization and movement inside live MCF-7 cancer cells, are demonstrated. These capabilities hold considerable promise for designing fuel-free nanoswimmers capable of performing complex tasks for diverse biomedical applications.