New diffractive imaging techniques using coherent x-ray beams have made possible nanometer-scale resolution imaging by replacing the optics in a microscope with an iterative phase retrieval algorithm. However, to date very high resolution imaging (< 40 nm) was limited to large-scale synchrotron facilities. Here, we present a significant advance in image resolution and capabilities for desktop soft x-ray microscopes that will enable widespread applications in nanoscience and nanotechnology. Using 13 nm high harmonic beams, we demonstrate a record 22 nm spatial resolution for any tabletop x-ray microscope. Finally, we show that unique information about the sample can be obtained by extracting 3-D information at very high numerical apertures.