I don't think I saw the beginning. A young man becomes the protegé of an older experienced hit man. They go on a mission and kill a few other young men (one is fat?) and he says he is too close, then the young hitman shoots and blood splatters on his face. It turns out the young man is very good and efficient and has no feelings, and starts to take business from his mentor. Eventually he has to kill his mentor, and while sitting at a table, his mentor says "You're too close" but he shoots and again blood splatters on his face. The young man falls in love with a woman, and while at her house, her abusive ex (?) boyfriend comes over and the young hitman pistol whips him and tells him to stay away and they share a cigarette (?). Eventually the young man decides he doesn't want to be a hit man any more so on his next visit to his boss while his boss is talking about a new job and making drinks, the young man just shoots him and the bodyguard. The young man and woman run away to a new life (?). The movies was from the 80's or 90's.
Though there are several mentor-protege hitmen films, I think Coldblooded from 1995 with Jason Priestley might fit. From IMDb:
As the title suggests, Cosmo's successful as a hitman because he has no feelings. Also, he hits Jasmine's abusive boyfriend in the face with a gun and offs the boss (played by Robert Loggia) in the end. Here's the (german-dubbed) trailer.