Imaging through scattering media remains a formidable challenge in optical imaging. Exploiting the memory effect presents new opportunities for non-invasive imaging through the scattering medium by leveraging speckle correlations. Traditional speckle correlation imaging often utilizes a random phase as the initial phase, leading to challenges such as convergence to incorrect local minima and the inability to resolve ambiguities in object orientation. Here, a novel method for high-quality reconstruction of single-shot scattering imaging is proposed. By employing the initial phase obtained from bispectral analysis in the subsequent phase retrieval algorithm, the convergence and accuracy of the reconstruction process are notably improved. Furthermore, a robust search technique based on an image clarity evaluation function successfully determines the optimal reconstruction size. The study demonstrates that the proposed method can obtain high-quality reconstructed images compared with the existing scattering imaging approaches. This innovative approach to non-invasive single-shot imaging through strongly scattering media shows potential for applications in scenarios involving moving objects or dynamic scattering imaging scenes.