Final Fantasy 13 How to beat "the proudclad" in chapter 12?

My characters have between 4.5k and 5.5k HP. I tried to beat him 5 times just now, each time the battle took around 15 minutes and i get him below half HP or so, and he heals ALL the way up. is it possible for me to beat this guy right now? and if not where is the most efficient place to farm up some CP?