I'm not sure if it's been mentioned yet- I don't think it has and the first post is still unclear- but I believe that unlocking Billy has nothing to do with target actions but rather the ranking shown at the end of the match.
I tried various amounts of target actions (ranging from none at all to a couple per round to just a few per match) and none of them got him to show up. It was only when I tried to just get hit as little as possible and managed two 'A' ranks and an 'S' on the run that he showed up on. I'm not sure which rank you would need to have him show (or even if this really is the determining factor) but it's worth a shot to find out if anyone hasn't unlocked him yet.
I tried various amounts of target actions (ranging from none at all to a couple per round to just a few per match) and none of them got him to show up. It was only when I tried to just get hit as little as possible and managed two 'A' ranks and an 'S' on the run that he showed up on. I'm not sure which rank you would need to have him show (or even if this really is the determining factor) but it's worth a shot to find out if anyone hasn't unlocked him yet.