Walnuts contain many helpful nutrients and healthy omega-3 fatty acids, which help your body fight inflammation that actually slow down the growth of breast cancer tumors. Research suggests that walnut is particularly effective at protecting your cells against environmental exposures that may increase the risk for cancer. Regular consumption of walnuts can help you keep breast cancer at bay. Heath experts suggest eating two ounces of walnuts in a day in order to slow down the development and growth of breast cancer tumors.