Short-term radar-based precipitation nowcasting is a critical component of real-time early-warning systems, especially in regions like Northwest Vietnam where the impacts of climate change are increasingly severe. Yet achieving reliable predictions several steps ahead while still preserving the spatial organization of rainfall patterns remains a substantial challenge for most existing approaches. This study introduces SR2-GAN, a Generative Adversarial Network tailored for multi-step radar nowcasting. The generator is built upon a ConvLSTM backbone enhanced with refined CBAM attention modules to better capture the dynamic features of rainfall. In parallel, the discriminator evaluates outputs at the patch level, encouraging the model to produce sharper and more coherent structures. A key aspect of the proposed framework is a composite multi-objective loss that jointly leverages adversarial learning, MSE, and SSIM. This design allows the network to balance pixel-level fidelity with the preservation of morphological characteristics. Experiments conducted on radar data from the Pha Đin station (Vietnam) and the DWD dataset (Germany) show that SR2-GAN significantly reduces MSE by 44.4