The Standard Model of Particle Physics (SM) describes the interactions between elementary particles and is the most fundamental theory of nature to date. Nonetheless, it cannot be a complete theory of nature, as it does for example not include gravity nor provide a candidate particle for dark matter. Supersymmetry is a well motivated and promising extension of the SM, providing a solution to some of its open questions. Supersymmetry could, for example, provide a candidate particle for dark matter.This research project aims to develop a search for supersymmetry in final states with one lepton, multiple quarks and weakly interacting neutral particles using proton-proton collision data taken by the ATLAS detector at the LHC at CERN. The signal models studied assume different electroweak production modes of charginos and next-to-lightest neutralinos decaying into W, Z and Higgs bosons as well as lightest neutralinos. Due to low cross-sections of the electroweak production of supersymmetric particles and the high similarity to SM backgrounds, many of these signal models only recently got into reach of the LHC experiments. Different signal regions targeting varying mass-splittings between the supersymmetric particles will be defined. All signal regions will be designed to be orthogonal to each other in order to allow simultaneous likelihood fits. Additionally, shape fits in discriminating observables will be employed in order to achieve sensitivity to a variety of other supersymmetric models. Furthermore, semi-data-driven estimations of the dominant SM backgrounds using dedicated control regions will be developed.The results of the search will either be the discovery of hints to physics beyond the SM or tightened constraints on supersymmetry model parameters. In any case, the results will allow particle physics to further inch its way toward the true nature of the fundamental building blocks of our universe.