The results of a soft X-ray chemically sensitive ptychographic imaging of non-planar nanoscale 3D objects - atom probe tomography tips, with resolution down to 12 nm at 800 eV using scanning X-ray microscope at the electron storage ring BESSY II are presented. We validate that this approach can be used to determine the tip (emitter) shape, and to resolve inner nano-scale structures as relevant for semiconductor applications and even for quantitative chemical composition analysis. Imaging of buried interfaces with below 30 nm resolution is demonstrated. This work might pave the way for contactless, ptychographic in-situ characterization of APT tips with tabletop coherent EUV sources.