A sanding sequence up thru 2000 will get it to very near-mirror, if it's done fully and correctly. A lot of sanding will be needed; with the scratches shown in the pics, you'll probably want to start pretty low in grit, in the 220/320 ballpark or so. Use a sanding block with wet/dry sandpaper (silicon carbide) and sand in a linear direction, like spine-to-edge or heel-to-tip. OR, do so on a sheet of wet/dry laid flat and secured to a smooth, flat surface, like wood or glass (I've used a granite reference plate for this). Alternate the sanding direction by 90 degrees with each step in grit, to make sure all scratches from the previous grit are replaced by the new grit's scratches. Keep the sequence tight in gradual steps, like 220/320 > 400 > 600 > 800 > 1000/1200 > 1500 > 2000. Should be near-mirror by 2000, after which some polishing with a paste like Simichrome, Flitz, etc will take it further and brighter. The back side of a clean sheet of wet/dry sandpaper can be used with the polishing paste in the same manner as was done for the sanding.
Alternatively, some denim, linen or canvas laid flat & tight to a hard surface can be used the same way, with the polishing compound. On the fabrics, some stick/crayon-type compounds made for use on powered buffers will work real well. Look for compounds labelled for polishing 'hard metals' or stainless steel specifically; such a compound would be something like white rouge (aluminum oxide), and grey or yellow stick-type compounds should also work well, again in aluminum oxide.
This is the sort of project that might be more easily done in steps over some time. A knife like that can be made to look pretty good just in the first 220/320 sanding step, producing a nice satin that emulates a lot of factory knives' finishes. Then, over time, you could take it up another grit or two in 'baby steps', so the job doesn't get too daunting.