In this computational study, the implementation of passive nonlinear vibro-impact attachments (termed nonlinear energy sinks (NESs)) for shock mitigation of an otherwise linear multistory large-scale structure is investigated. This is achieved by inducing passive targeted energy transfer (TET) from the fundamental (lowest-frequency and most energetic) structural mode to high-frequency modes, through a series of vibro-impacts induced by the attachments. The functionality of the passive attachments is based on single-sided vibro-impacts (SSVIs), enabling rapid and one-way scattering of shock energy from low- to high-frequency structural modes. Hence, redistribution of shock energy in the modal space of the structure occurs as energy gets nonlinearly scattered to high frequencies. In turn, this energy scattering rapidly reduces the overall amplitude of the transient structural response, and increases the effective dissipative capacity of the integrated NES-structure assembly. The effective modal dissipation rates of the integrated assembly can be controlled by the inherent damping of the NESs, and can be qualitatively studied in detail by defining appropriate dissipative measures which track the TETs from low- and high-frequency structural modes. Ideally, the optimized NESs can passively scatter up to 80% of the input shock energy from the fundamental structural mode to high-frequency modes in the limit when their inherent damping is zero and the coefficient of restitution during vibro-impacts is unity. When dissipative effects are introduced into the NESs, additional energy exchanges between the NESs and high-frequency modes occur. Our study facilitates the predictive design of vibro-impact NESs for optimal and rapid shock mitigation of large-scale structures.