We investigate the electronic structure of the highly anisotropic $beta$ phase of metallic plutonium, within the combination of density functional theory (DFT) and dynamical mean field theory (DMFT). Its crystal structure gives rise to site and orbital selective electronic correlations, with coherent Pu-5$f_{5/2}$ states and very incoherent Pu-5$f_{7/2}$ states. The Hunds coupling is essential for determining the level of correlations of electrons in Pu-5$f$ states, and for the quasiparticle multiplets features in the Pu-5$f$ spectral function.