Nature utilizes the available resources to construct lightweight, strong and tough materials under constrained environmental conditions. The impact surface of the fast-striking dactyl club from the mantis shrimp is an example of one such composite material; the shrimp has evolved the capability to localize damage and avoid catastrophic failure from high-speed collisions during its feeding activities. Here we report that the dactyl club of mantis shrimps contains an impact-resistant coating composed of densely packed (about 88 per cent by volume) ~65-nm bicontinuous nanoparticles of hydroxyapatite integrated within an organic matrix. These mesocrystalline hydroxyapatite nanoparticles are assembled from small, highly aligned nanocrystals. Under impacts of high strain rates (around 10⁴ s^-1), particles rotate and translate, whereas the nanocrystalline networks fracture at low-angle grain boundaries, form dislocations and undergo amorphization. The interpenetrating organic network provides additional toughening, as well as substantial damping, with a loss coefficient of around 0.02. An unusual combination of stiffness and damping is therefore achieved, outperforming many engineered materials.