A search for weakly-produced Chargino1, Neutralino2 supersymmetric particles decaying to two final state electrons or muons with the same electric charge is presented. The analysis is performed on 20.3\ifb~of integrated luminosity collected in 2012 with the Atlas Detector at the Large Hadron Collider, running at $\sqrt{s} = 8$ TeV. Pairs of like-sign leptons are collected and discriminated against background using Boosted Decision Trees trained on compressed supersymmetric simplified models. No significant excesses above background expectations are observed. The 95% confidence limits are placed on Chargino1 Neutralino2 pairs decaying via W and Z bosons and via intermediate sleptons with two different assumptions on the relative slepton mass. In the most optimistic scenarios considered, Chargino1 below 410 GeV are excluded assuming a massless LSP. In the compressed scenario, Chargino1 $< 180$ GeV are excluded, with $\Delta$M Chargino1, LSP $>20$ GeV. Results from this analysis are also combined with those from a complementary search in the three lepton final state.