The Standard Model of particle physics is a successful theory, yet it is incomplete. Supersymmetry is one of the favoured extensions of the Standard Model, elegantly addressing several unresolved issues. This thesis presents a search for the pair production of supersymmetric particles chargino one and neutralino two, where the neutralino two decays to the lightest neutralino and the 125 GeV Higgs boson. The final states considered for the search have large missing transverse momentum, an isolated lepton and two jets identified as originating from bottom quarks. The analysis is based on 20.3 inverse femtobarns of 8 TeV proton-proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. No excess over Standard Model predictions is observed. The analysis has been combined with three independent searches that probe other decay modes of the Standard Model Higgs boson. Limits are set at 95% confidence level in the context of a simplified supersymmetric model. Common masses of chargino one and neutralino two are excluded up to 250 GeV for a massless neutralino one. The analysis of this dissertation has been reinterpreted in the context of a large scan of the phenomenological Minimal Supersymmetric Standard Model, along with 22 other ATLAS Run 1 searches. The resulting summary paper represents the most comprehensive assessment of the ATLAS constraints on Supersymmetry models to date. / Graduate / 0798 / cdavid@uvic.ca