To me, the phrase "win over" means "to convince someone to change their mind." It implies persuasion, not force. It is not the same as winning a game or winning a war. It implies persuasion, not force. This gentle meaning is also seen in "He had a winning smile." (It makes you like him and smile back). "He had winning ways." (Everybody likes him). "At the beginning, everyone at the meeting was opposed to John's idea, but he was able to win them over." I think it's perfectly OK to use it in the context of courtship: "At first Elizabeth hated Mr. Darcy, but in the end he won her over." OBSOLETE USAGES: A century ago, in books set in the U.S., you do read about men being called "lady-killers" and bragging of their "conquests." We do NOT speak that way any more. There is a saying FROM ABOUT THE 1600s(!) which has made it into modern English as "Faint heart never won fair lady."

Yes, it is a perfect translation for conquistar a una chica. I don't think it is necessarily not politically correct. You could say John finally won over Amanda with all of his with all of his kind gestures towards her. ( como detailles) and I don't think that is negative. To conquer, which would be a literal translation from Spanish would sound "politically incorrect"!

To win a girl over is correct. In the U.S. it is used often and perfectly acceptable. You can also use the phrase for anyone who had a different idea or preference as you if they have changed their minds. For example, "John wanted to watch X-Men with the guys, but I won him over when I mentioned there would be dessert at my work party." This means that John decided to go to his spouse's work party after he realized he would have good food. He changed his mind due to new information, so his spouse "won him over."

"to win over a girl" is a phrase I've heard, however, it is now associated with macho culture and isn't politically correct.