Streets of Rage 2's ultra-masculine first boss pops up briefly behind the bar in the background, before deciding to step outside and take care of some unfinished business. Barbon stays behind the bar until you get close enough to trigger the miniboss in front of the bar. At which point he walks out back. Undaunted by the hurling rain, Barbon rips off his shirt to reveal an impressive physique and black belt and sets forth to demolish the players with some very impressive footwork.
While not especially difficult, Barbon is a respectable opponent with a great reach when it comes to kicks and throws and the sort of moustache that we sadly don't see enough of these days. Barbon will stay completely stationary until you get to a certain distance from him. For Mania playthroughs this can be taken advantage of by defeating all of his minions before you fight him, which could help make it easier for you to reach the Turkey in case of emergency.
After being vanquished, Barbon is succeeded later in the game by several identical twins with the same abilities but different names and colour schemes.
A point of interest to anyone wanting to bring the burly barman down quicker is that Barbon's ability to block can backfire. Certain attacks like Skate's Corkscrew kick and Max's shoulder charge actually do far more damage to Barbon when defended than when they strike clean. While both of those moves take some life from the user, the risk is usually worth it. Axel's Grand Upper has the same effect, since Barbon's block makes the uppercut hit multiple times the damage adds up to be greater than an unblocked hit. This particular method of defeating him is probably the easiest, since using the Grand Upper attack costs no health.
While it is a reasonable assumption that Barbon is part of the Syndicate, there is always the chance that he's just understandably annoyed about Axel and pals wrecking his bar. Although, who would want a bunch of lowly thugs hanging around their clientele?