The bold is the problem. You are thinking too much, which is psyching you out. You need to approach as a natural reaction. I know it's easier said than done, but it still holds true.
Most of the time AA stems from a fear of rejection. You wouldn't be nervous to approach someone if you didn't care about the outcome. So, you need to do 1 of 2 things: 1) Get rejected enough times it no longer bothers you, or 2) Change your thoughts on rejection in the first place.
Realize that getting rejected does nothing to you, unless you make it bother you. If you asked a stranger for $5 and they said 'no', would you spend the next 2 days crying about it? So if you ask a stranger for a phone number and they said 'no', big deal? You move on and find someone else to ask. Rejection has no intrinsic pain to it. The only way it hurts is if you let it. Try to become numb to it, or realize it's just part of the game.
Another thing is, when you see a girl, realize that in most cases, you've already seen her best side. Many times a very attractive girl will drop in value once you learn more about her. Whether it's because shes dumb as rocks, bad kisser, bad in bed, has a boyfriend she won't leave, or simply isn't your type.
So, instead of approaching a girl as "wow, she's beautiful! I would love a chance to take her out!"... think of it as "she's pretty cute, let's see if she fits what I'm look for". That way, you aren't putting her on a higher level than yourself. You are going into the situation as you should: looking for what YOU want. Not trying to give her what she wants.