If you attempt to "tailor" your introduction to some 'estimation' of what you believe she will respond favorably to based on looks or body language, you're going to wind up saying something really dumb.Okay, I don't know how to do this so I figured I would go to the place that would give me the most options. How do I go up to a girl I find attractive, but who doesn't know me and I don't know her and introduce myself?
Pick one introduction and use it every time for every girl in every casual situation.
Using this method, as long as it is not "Hey nice boobs you have there" or something clearly offensive, you may not "connect" with every girl, but you will connect with some of them.
I don't know if you're a fan of country, but there is a song that goes "Some girls don't like boys like me, but some girls do." That should be your motto.
You can't be all things to all people all the time, don't waste your time trying. Some girls will find you interesting, some girls won't. That's the way it goes.