The mantis shrimp is recognized to have one of the most powerful vision systems in nature, with up to 16 color-perceiving channels and the perception of linear and circular polarization detection. Inspired by its biostructure, we developed a snapshot polarization-hyperspectral camera (pHScam) to detect linear polarization in four directions and spectral signature in 21 bands of incident light, resulting in a 4D polar-spectral hypercube, represented as H(x,y,l,S→). We introduced two bio-mimetic encoding mechanisms, viz., two-tier color encoding and pixelwise mosaic polarization encoding, to efficiently compress the original 4D datacube into a 2D mosaic raw pattern. The full-resolution recovery is solved by convex optimization algorithm, utilizing known prior sparsity and experimental system calibrations.