In my opinion, the only way to get around apporach anxiety, is doing a lot of approaches. But as PlayHer Man already advised, take baby steps. It's like a muscle that you build up. You don't start with the heavy weights, but with smaller ones and then build it up.
I had a time in which I didn't do any approaches for a couple of months, and when I got back into the Game, my AA was basically at the same level where it used to be (which was really bad). In fact, it was probably even worse, because I was supposed to know all this stuff and get good results, which fucked me up even more. So I went back to basics and imposed newbie missions on myself. Here is my workout plan:
First round: You have 12 minutes to approach 10 sets. Walk up to them, say something like "Hi, how is it going, have a merry Christmas ..." and walk away. Your goal is not to start a conversation, but simply talk AT them and walk away. The time constraint is key here. It sets a goal that has nothing to do getting the girl. It makes you independant of the outcome.
Second round: Same time, same amount of sets. Use an indirect opener. Ask their opinion about something, let them answer and leave.
Third round: Same time, same amount of sets. Use a direct opener. Walk up to a girl, make her a compliment (I like your outfit/ style/ whatever else or simply say that you think she is cute/ gorgeous/...) and leave. You don't need to wait for a reaction. The point is to simply force yourself to do it.
Fourth and last round: This time there is no time limit, but do this at least five times. Use a direct opener on a girl that is surrounded by people (for example at a busstation).
I did this a short time ago on a shopping street during the Christmas period. It is best to have a wing with you who can hold you accoutnable. You can also think up creative punichments in case you don't make it in the time limit. This plan was inspired by the website
www.mypuajourney.com. But I adapted it to my specific needs.
Have fun,
Nemo