Imaging dynamic strongly scattering scenes remains a significant challenge because it is typically believed that moving objects and dynamic media provide huge barriers. Instead, we use the dynamics of objects and media and put forward a recursion-driven bispectral imaging (ReDBI) framework here for the reconstruction of a stationary or moving object hidden behind the dynamic media. ReDBI avoids the errors introduced by speckle modulation and phase-retrieval algorithms in the existing studies. We also quantitatively assess the reconstruction difficulty of character and shape objects with the benchmark of the minimum number of speckle images (MNSI) required to achieve a high-quality reconstruction, which can help to comprehend the media's transfer properties.