This paper introduces a data-driven approach to estimate precipitation rates from Synthetic Aperture Radar (SAR) at a spatial resolution of 200 meters per pixel. It addresses previous challenges related to the collocation of SAR and weather radar data, specifically the misalignment in collocations and the scarcity of rainfall examples under strong wind. To tackle these challenges, the paper proposes a multi-objective formulation, introducing patch-level components and an adversarial component. It exploits the full NEXRAD archive to look for potential co-locations with Sentinel-1 data. With additional enhancements to the training procedure and the incorporation of additional inputs, the resulting model demonstrates improved accuracy in rainfall estimates and the ability to extend its performance to scenarios up to 15 m/s.