In photon upconverting core-shell nanoparticles, structure strongly dictates performance. Typical imaging in scanning transmission electron microscopy has sufficient resolution to probe the atomic structure of these nanoparticles, but contrast, dose, and projection limitations make conventional methods insufficient for fully characterizing these structures. Phase retrieval techniques provide a promising alternative imaging mode, and, in particular, multislice electron ptychography can recover depth-dependent information. Here, we study beam-sensitive photon upconverting core-shell nanoparticles with a multislice ptychography approach using a low electron dose to avoid damage. Large strain fields arise in these heterostructures due to the mismatch in lattice parameter between the core and the shell. We reconstruct both a nanoparticle that appears defect-free and one that has a large break in the side and map the distribution of strain in 3D by computing distortion fields from high-resolution potential images of each slice. In the defect-free nanoparticle, we observe twisting of the shell, while in the broken nanoparticle, we measure the 3D position of the crack, the core, and dislocations. These results highlight the advantage of multislice electron ptychography to recover 3D information from a single scan, even under strict electron dose requirements from beam-sensitive samples.