While new forms of attacks are developed every day to compromise essential infrastructures, service providers are also expected to develop strategies to mitigate the risk of extreme failures. In this context, tools of network science have been used to evaluate network robustness and propose resilient topologies against attacks. We present here a new rewiring method to modify the network topology, improving its robustness, based on the evolution of the network's largest component during a sequence of targeted attacks. In comparison with previous strategies, our method lowers by several orders of magnitude the computational effort necessary to improve robustness. Our rewiring also drives the formation of layers of nodes with similar degree while keeping a highly modular structure. This ‘modular onion-like structure’ is a particular class of the onion-like structure previously described in the literature. We apply our rewiring strategy to an unweighted representation of the World Air-transportation network and show that an improvement of 30% in its overall robustness can be achieved through smart swaps of around 9% of its links.