Synchronous Rain streaks and Raindrops Removal (SR3) is a very hard and challenging task, since rain streaks and raindrops are two wildly divergent real-scenario phenomena with different optical properties and mathematical distributions. As such, most of existing deep learning-based Singe Image Deraining (SID) methods only focus on one of them or the other. To solve this issue, we propose a new, robust and hybrid SID model, termed Robust Attention Deraining Network (RadNet) with strong robustenss and generalztion ability. The robustness of RadNet has two implications :(1) it can restore different degenerations, including raindrops, rain streaks, or both; (2) it can adapt to different data strategies, including single-type, superimposed-type and blended-type. Specifically, we first design a lightweight robust attention module (RAM) with a universal attention mechanism for coarse rain removal, and then present a new deep refining module (DRM) with multi-scales blocks for precise rain removal. The whole process is unified in a network to ensure sufficient robustness and strong generalization ability. We measure the performance of several SID methods on the SR3 task under a variety of data strategies, and extensive experiments demonstrate that our RadNet can outperform other state-of-the-art SID methods.