I may never know why talking about SELPH is such a hot button issue here, but I just want to give my thoughts on what SELPH's fight may have been like, by piecing together various bits of information. Here's what the Wiki says;
Another nugget of information discovered were parts for a sort of "mirror staff" and additional information regarding the data, found by another hacker.
Selph's AI was supposedly used to make it possible for Claris to appear in Elliot's Wizeman battle, which leads fans to believe that Selph would have had a battle similar to Reala's.
A mirror staff, and her AI being used for the Wizeman battle, make it seem very much like SELPH may have been just as unconventional of a boss as many others in NiD. What I think would happen, based on this information, is that SELPH would have a short, in-game opening cutscene directly before his battle, similar to Reala, in which he would use his mirror staff to look exactly like NiGHTS, and then begin following her around. The Wizeman battle partner AI has a very slightly differently coloured NiGHTS on a basic follow path, locked to NiGHTS, so theoretically, there would supposedly be an obstacle, which the player would have to fly directly at, and then air brake or maneuver away from at the last second to have NiGHTS SELPH crash into it. After this, SELPH would possibly use her mirror staff again to transform back into his true form, and rush NiGHTS head-on. If NiGHTS is able to avoid this attack, SELPH uses her mirror staff once more to transform back into NiGHTS SELPH, and the pattern would repeat once more before defeat.