This is one of the best films I've seen in my life, with beautiful cinematography, excellent acting, and most importantly, a great script. It's sad to see that some of you are too busy critiquing the lack of complexity in the plot, because it is this simplicity that makes this movie so beautiful.
Since many of you have already reiterated the plot, i'll just cut the chase and try to clear up some confusion, hopefully.
First of all, to understand why he let the girl go and turns against his boss, the flashback towards the end is very crucial. When she plays the cello, he smiles, and as he is dying, he smiles as he listens to her voice. These are the only two occasions in which he smiles throughout the entire movie. Whether this is love, attraction, or because he was thankful that she made him feel good, is open to interpretation. Given that he is an extremely straightforward and honest character(and also given that in this movie, everything is what you see on the screen- there are no hidden motives, twists, whatsoever), I assume that the reason he doesn't answer (or CAN'T answer) when asked why he did it by his boss is because he doesn't know himself.
I think the key to understanding this movie is the title, and the narration at the end of the movie (something along the line of a disciple telling his master that he cries after a sweet dream because he knows it can't come true). For Sunwoo,the girl and his belief(?) that he can kill everyone else and still live are sweet dreams that cannot come true. The reason why he unrealistically gets by after getting shot and stabbed so much, is not simply because he is the main character, but because everything he does after meeting the girl is like a sweet 'dream', a surreal reality(yes, an oxymoron, just like the title- a 'bittersweet' life). The morbid ending is also very fitting- as sweet as the dream was, the more bitter it is when he "wakes up" from it and faces reality(once again relating to the last narration).