High resolution imagery of the Sun's X-ray corona provides an essential clue in understanding dynamics and heating processes of plasma particles there. However, X-ray imagery of the Sun with sub-arcsecond resolution has so far never been conducted due to severe technical difficulty in fabricating precision Wolter mirrors. For future X-ray observations of the solar corona, we are attempting to realize precision Wolter mirrors with sub-arcsecond resolution by adopting advanced surface polish and metrology methods to sector mirrors which consist of a portion of an entire annulus, by direct polishing onto the mirror substrate.Based on the knowledge obtained through fabrication of the first (in 2013) and second (in 2014) engineering Wolter mirrors and subsequent evaluations on their X-ray focusing performance, the third engineering mirror was made in 2015−2016. The primary target of improvement over the second mirror was to suppress figure error amplitude especially for spatial frequencies around 1 mm -1 and to suppress the large astigmatism that was present in the second mirror, by introducing improved deterministic polish and smoothing on the precision mirror surfaces (32.5 mm × 10 mm in area for both parabola and hyperbola segments), as well as by careful characterization of the systematic error in the figure measurement system for the precision polish. Measurements on the focusing performance of thus-fabricated third Wolter mirror at SPring-8 synchrotron facility with 8 keV X-rays demonstrated that the mirror attained sub-arcsecond focusing performance with its HPD (half-power diameter) size reaching as small as ~0.2 arcsec for meridional focusing while ~0.1 arcsec for sagittal focusing. The meridional focusing achieved nearly diffraction limited performance (~0.12 arcsec FWHM for the PSF core). We also confirmed that the large astigmatism noted in the second mirror was correctly removed in the third mirror with the correction of the above-mentioned systematic error.