Early detection of tumor tissue is one of the most significant factors in the successful treatment of breast cancer. Microwave breast imaging methods are based on the dielectric contrast between normal and cancerous tissues at microwave frequencies. When the breast is illuminated with a microwave pulse, the dielectric contrast between these tissues can result in reflected backscatter. These reflected signals, containing tumor backscatter, are spatially focused using a beamformer which compensates for attenuation and phase effects as the signal propagates through the breast. The beamformer generates an energy profile of the breast where high energy regions suggest the presence of breast cancer. Data-Adaptive (DA) beamformers, use an approximation of the desired channel response based on the recorded signal data, as opposed to Data-Independent (DI) algorithms which use an assumed channel model. A novel extension of the DA Robust Capon Beamformer (RCB) is presented in this paper which is shown to significantly outperform existing beamformers, particularly in a dielectrically heterogeneous breast. The algorithm is evaluated on three anatomically accurate electromagnetic (EM) breast models with varying amounts of heterogeneity. The novel beamforming algorithm is compared, using a range of performance metrics, aganist a number of existing beamformers.