The shockwave produced alongside the plasma during a laser-induced breakdown spectroscopy event can be recorded as an acoustic pressure wave to obtain information related to the physical traits of the inspected sample. In the present work, a mid-level fusion approach is developed using simultaneously recorded laser-induced breakdown spectroscopy (LIBS) and acoustic data to enhance the discrimination capabilities of different iron-based and calcium-based mineral phases, which exhibit nearly identical spectral features. To do so, the mid-level data fusion approach is applied concatenating the principal components analysis (PCA)-LIBS score values with the acoustic wave peak-to-peak amplitude and with the intraposition signal change, represented as the slope of the acoustic signal amplitude with respect to the laser shot. The discrimination hit rate of the mineral phases is obtained using linear discriminant analysis. Owing to the increasing interest for in situ applications of LIBS + acoustics information, samples are inspected in a remote experimental configuration and under two different atmospheric traits, Earth and Mars-like conditions, to validate the approach. Particularities conditioning the response of both strategies under each atmosphere are discussed to provide insight to better exploit the complex phenomena resulting in the collected signals. Results reported herein demonstrate for the first time that the characteristic sample input in the laser-produced acoustic wave can be used for the creation of a statistical descriptor to synergistically improve the capabilities of LIBS of differentiation of rocks.