So since people have been experimenting with the game and sharing their results here, I'll tell you what I just found out.
You can actually beat Scarlett the very first time you fight against her without having to use any kind of cheating. You have to get extremely lucky, though, and it could take a lot of grinding.
The way you do it is by having your attacks critting at least 3 times, and having scarlett do the armpit move in her grappling turn. I don't know what the odds are for your attacks doing critical damage, if I had to go on a limb I'd say they feel like they have a 1 in 20 chance to crit. You obviously have to guard when she does her triple kick, but the rest of the time you'll be using your attacks fishing for crits.
I doubt anyone is as insane as I was to try and do this, but at least it's interesting to know that you can actually go through the game without losing to anyone, the ultimate invict blue-balls playthrough is possible!