Accurate pose estimation and shift correction are key challenges in cryo-EM due to the very low SNR, which directly impacts the fidelity of 3D reconstructions. We present an approach for pose estimation in cryo-EM that leverages multi-dimensional scaling (MDS) techniques in a robust manner to estimate the 3D rotation matrix of each particle from pairs of dihedral angles. We express the rotation matrix in the form of an axis of rotation and a unit vector in the plane perpendicular to the axis. The technique leverages the concept of common lines in 3D reconstruction from projections. However, common line estimation is ridden with large errors due to the very low SNR of cryo-EM projection images. To address this challenge, we introduce two complementary components: (i) a robust joint optimization framework for pose estimation based on an $\ell_1$-norm objective or a similar robust norm, which simultaneously estimates rotation axes and in-plane vectors while exactly enforcing unit norm and orthogonality constraints via projected coordinate descent; and (ii) an iterative shift correction algorithm that estimates consistent in-plane translations through a global least-squares formulation. While prior approaches have leveraged such embeddings and common-line geometry for orientation recovery, existing formulations typically rely on $\ell_2$-based objectives that are sensitive to noise, and enforce geometric constraints only approximately. These choices, combined with a sequential pipeline structure, can lead to compounding errors and suboptimal reconstructions in low-SNR regimes. Our pipeline consistently outperforms prior methods in both Euler angle accuracy and reconstruction fidelity, as measured by the Fourier Shell Correlation (FSC).