This game is highly conducive to speedrunning, because most of what it takes to defeat the sphinx is also used to beat the other enemies quickly - namely, building attack power as quickly as possible to outrun your opponent with crush attacks. There are also no known glitches that would necessitate a separate "glitchless" category - the one thing it could maybe use is a variable of whether items were used (My speedrun used items.)
But there may be a few subtle differences between "dueling" (playing the game normally) and speedrunning this, having mostly to do with aggression levels.
If I were playing for my life against a weak to mid-strength enemy (the presumed storyline in the game), I would play a bit more conservatively to make sure I win (or minimize my chance of losing.) If, however, I were speedrunning, the run sort of dies anyway if I lose, and in fact it can be better to lose one round quickly than have a long, drawn-out battle ending in victory! So it's better to be overly aggressive for the strength of your opponent, and I did my speedrun basically treating all enemies like the sphinx.
Speedrunning might even help me defeat the sphinx, because I'm already used to the aggression necessary to beat it, and I also have very little time to get nervous going into the sphinx. The only difference at the sphinx is that I use my items first when useful, rather than saving them for the last attempt to give myself a few chances to beat it itemless before resorting to the items. Or if in a time crunch to break 30 minutes or something, I might even play the sphinx like it were the WR holder...
My thread about "no active moderators?" has a link to my run, still awaiting approval. Unofficial time: 30:16.98.
What i noticed after playing a lot of vs matches on fightcade is that not only you have to be faster than your oponent, you also have to be aware of your oponent screen in case they got a magic jewel, so you can crush it with your attack. In speedrunning is not really necessary to do this because only the sphinx could destroy your magic jewels.