The advancement of additive manufacturing technologies has enabled the realization of complex geometries necessary for novel metamaterials, which can be used as passive wave transforming structures in applications ranging from acoustics to impact mitigation and vibration isolation. Nonlinear metamaterials offer significant performance enhancements by leveraging mechanisms such as snap-through instabilities and energy-locking bistability, however, current methods predominantly focus on periodic configurations and quasi-static scenarios, limiting their potential for dynamic performance. In this work, we present a generative bilevel optimization framework for designing nonlinear metamaterial systems tailored for impact mitigation. The multiscale approach exploits nonlinear dynamics at the macroscale and large deformations at the mesoscale to achieve the desired dynamic response. The macroscopic system is modeled as a one-dimensional mass-spring-damper chain, where the unit cell nonlinearities are represented by polynomial force-displacement relations. Discrete element modeling (DEM) is used to simulate the impact dynamics of the system, allowing us to identify the optimal nonlinearities that maximize dynamic performance metrics such as minimizing the peak transmitted kinetic energy or the maximum force in the structure. We further investigate the effects of spatial disorder, damping and impact conditions on dynamic wave attenuation. Subsequently, the DEM-identified mechanical responses guide the mesoscale unit cell design using level-set topology optimization (LSTO). Incorporating finite element analysis with large deformations and material nonlinearities, LSTO identifies geometries that reproduce the targeted nonlinear force-displacement response for each unit cell. Our findings through simulations and experimental validations demonstrate that nonlinear metamaterials can significantly outperform their linear counterparts, reducing transmitted kinetic energy by up to two orders of magnitude. The high sensitivity of dynamic performance to minor variations in nonlinearities and the intricate features of the unit cell designs underscore the necessity of precise geometric control offered by additive manufacturing technologies.