Why didn't the boss kill the girl?
Maybe this has been asked before but as I understood it Kim was supposed to kill the girl if he found out she was cheating.
The boss took revenge on Kim because he realized there must have been a reason Kim let the girl live and lied about the fact that she DID have an affair.
Why did HE(the boss) let the girl live? When he visited her after she was already instructed by Kim not to see her lover again, the boss realized by her reaction that something was off which probably led to his suspicion that Kim lied to him. Kim also told his boss directly about the affair(at the moment when he was supposed to be killed and had a last chance to speak to his boss on the cell phone).
You would assume that the boss would have the girl assassinated after that.