In this paper, the mechanical behavior of bio-inspired nacre-like staggered composites is studied. The bio-inspired materials, combining stiff and soft constituents, exhibit superior mechanical properties. Here, the attention is focused on the competing properties: penetration resistance and flexibility of the composites. To this end, a novel hybrid multiscale method is developed, combining a hierarchical multiscale approach with a concurrent approach. The method allows to perform accurate parametric nonlinear analyses at a low computational cost. The influence of the microstructural parameters (i.e., platelet aspect ratio and volume fraction) on the macroscopic mechanical behavior is thus analyzed. Finally, the potential of achieving tailored protective properties and flexibility through microstructural design of the bio-inspired composites is illustrated.