Barbon is trivial on easy difficulties, but could be a bit tricky on higher ones. Just try and get rid of his goons before he rips off his shirt. Jump kicks and directional specials are a good way to take him down quickly.
Here's a few points to remember:
Barbon has a throwing move and he's not shy on using it on higher difficulties. There's an easy counter; if you are thrown by any enemy, simply hold up and jump while in the air until you land, and you'll be on your feet with no damage.
Barbon is an opportunistic fighter; he'll hang back for a little bit, and then rush in for a quick combo. You can be faster on the punch when he comes in, but specials are more reliable, and Offensive Specials hurt even more.
Approach slowly when you're about to face him to trigger his minions first. They're not too much trouble, but it always helps to keep the battlefield clean of distractions.
Don't forget the chicken in the trash bin if you're in trouble.