I'm a noob, but I think I am pretty much over approach anxiety. The way I beat it was by figuring out what was causing the anxiety then solving it in steps. I realized that 95% of my anxiety came from the fear of awkward silences. I was worried about not knowing what to say and not knowing how to recover from an awkward silence if I end up in one. So in the beginning, I had about 5 "back up" questions memorized to ask the girl when we ran into a conversational dead end. I think the most I ended up using was like 3.
Here's a run-down of how I beat the root of my anxiety, in case anyone reading this is also afraid of awkward silences. How I beat APPROACH anxiety comes afterwards. You can scroll down if you're not afraid of awkward silences.
1. This was at a party/kickback/mixer with a sorority. I basically went around introducing myself to 10-15 girls. Literally, all I did was say "Hey I'm fsc, what's your name? [she responds] Nice to meet you", then I would immediately move onto an adjacent girl and do the same thing. Do something simple like that to get your social momentum rolling. Have an interaction that is destined to close. Ask a girl where the bathroom is, for example, if you're at a mall. Then once the girl replies, just thank her and bounce. I repeated the introductions until I reached a dead end--it was just a girl and me on the patio with no one else around us, so I had to move onto a conversation. This led directly to #2...
2. Have polite/non-sexual/standard/boring conversations--yes, have BORING, retarded conversations. It's sort of like the "you have to fail before you know how to succeed" kind of things. Go YOLO/IDGAF and purposely fail so that you realize it doesn't feel so bad after all. It won't matter one bit in the end. Most of the guys the girl talks to probably give her a boring conversation anyway (the guys probably talk a lot about themselves). I used to pressure myself into coming up with interesting shit to talk about, but for now just converse about stuff like "what do you study?", "where are you from?", "what do you do in your free time?", etc. However, remember to actively listen, deep dive, and keep the conversation about her. Of course I ran into awkward silences because those are boring topics with no sexual or creative or emotional stimulation. I WELCOMED IT because I knew there was no easy way to succeed, and I had an escape route. The escape route was basically "do you want to play pool?" If she joined then we played, and I had time to think of another conversation thread while playing; if she declined, then I exited myself by saying something like "nice meeting you, I'm gonna go find someone to shoot pool with". Playing pool (or doing any activity) gives the girls a chance to come up with stuff to say as well. I used to think girls were natural social creatures, but I've since learned that girls can be hella shy and hella socially awkward too.
3. I've had boring conversations with girls for a while. Then I started throwing in compliments, touching, sexual innuendos, and social pressure. When I reached an awkward silence, instead of getting all panicky to come up with shit to say, I would just be calm, smile, and look at the girl right in her eyes. I would sometimes recollect our conversation up to that point and try to recall a conversational thread that I can resume and deep dive, but other times I just stood there with a blank mind. After a few seconds the girl would either excuse herself and bounce, or she would restart the conversation by asking me a question. Sometimes you can actually see the panic in the girl as she tries to revive the conversation, which can be kinda amusing. Note that because I've kept the conversation mostly about her up to that moment, she is now able to ask me about myself. Then I would give a detailed response (without laying everything on the table, of course) and try to turn the conversation back to her like
Her: ...soo...where are you from?
Me: I'm from fsc.hometown.
At this point I could be like "have you ever been there?" or "my hometown is known for this and that. Have you tried this and that? What is your hometown known for?" and blah blah
4. This is where I am at right now. I usually start off with a standard conversational topic, then deep dive off from there. If I end up at an awkward silence, I either put the pressure on her to talk (because up to that moment I've been the one getting her to talk about herself) or ask her one of my back up questions/topics, from which I can also deep dive. I've had a few interactions in which the conversation was mostly straight up random/weird shit like talking about roofie-ing people and selling their organs, or just straight up flirting. I am currently trying to get my conversations more like this because it's much more fun and less interview-like.
Beating approach anxiety
1. Most of my approaches have been something like "Excuse me, I think you're really attractive. Are you single by any chance?" After you get your social momentum rolling (kinda talked about in #1 above), it's simple enough to do. Initially, don't even worry about pre-opening or sexy smile or sexy eye contact or whatever. Just go YOLO/IDGAF and spit that line. Get it done. Unless you look like Danny Trejo, you won't be creepy enough for the girls to alert mall security. Eventually start being conscious about your eye contact and smile. It'll be a hit or a miss. The 2 chicks it worked on for me were totally hooked onto me and DTF, but most of the girls responded by telling me that they were taken in one way or another--"I have a boyfriend" or "I'm seeing someone"--at which point you can just exit gracefully. You'll likely get a lot of those rejections early on because your fundamentals will probably be off, but eventually you'll grow a thicker skin and learn to laugh it off. If she does say she's single, then simply ask what she's up to and make a conversation. If the conversation feels like it's headed to a dead end, propose a date before an awkward silence happens, number close, then bounce. Furthermore, I personally don't like to do a shit ton of approaches because it doesn't feel genuine to me. I only approach girls I am legitimately attracted to because then I'd be automatically smiling and I'd actually want to date her and bone her. Otherwise, the non-genuine feeling would probably kill my vibe, be guaranteed rejections to every single approach, then just end up feeling like crap. When I approach girls I like and get rejected, on the other hand, I actually get pumped up.
2. I am now trying to do more situational, indirect direct, or just generally slow (starting off with a conversation) openers now because the direct opener I mentioned above can feel impersonal. I believe it makes some girls feel like they're just another number to a heartless womanizer robot. I'm trying to have the mindset that I'm giving the girls an experience they only thought existed in romance novels and films. I want to cater the approach to the girl and make her feel special. In addition, the next time a girl tells me she's taken and doesn't take off, I'm gonna try persisting with a conversation.
If tl;dr, take baby steps. No one jumps straight to the top of Everest. We all climb one step at a time.