Picosecond opto-acoustic micro-spectroscopy is an optical technique based on ultrafast pump-probe generation and detection of hypersound on time durations of picoseconds and length scales of nanometers. This work reports on a dual-probe architecture to carry out real-time parallel detection of the hypersound propagation inside a transparent sample and, simultaneously, of the hypersound reflection at a metal/sample interface. This dual architecture offers unprecedented possibilities to image, at a micron scale, the mechanical properties of a non-homogeneous transparent material. We will show that, using this dual- optoacoustic modality, several biomechanical properties of a cell can be measured in a non-contact and label-free manner. The technique capabilities are notably illustrated with the imaging of multiple biomechanical properties of a mitotic macrophage-like cell, in a single run experiment. [1] Liu L., Plawinski L., Durrieu M-C, and Audoin B., "Label-free multi-parametric imaging of single cells: dual picosecond optoacoustic microscopy", Journal of Biophotonics 12(8), e201900045, 2019 doi:10.1002/jbio.201970028