I have done a couple of mirror finishes, and all I did was hand sand up to 2500 grit, making sure to sand out all the scratches from the previous grit and kept rotating my sanding direction 90 degrees from the last grit. No dirty sanding either, where you scrub back and forth, only draw/push in the one direction. For me that is push up from the edge to the spine and draw down from the handle to the tip.
Other tips I can offer is change your paper often, treat it like it was free.
Wet sand.
Thoroughly clean between grits, so there is nothing left laying around on your work, work space, hands, or sanding paddle.
And of course don't sharpen the edge till you have everything else done because doing it earlier will mean a trip to the doctor for stitches.