Despite the many insecurities I still struggle with, I've used to cope with my fear both on the mat and in life. Here are a few things that help me.
Just do it. (Nike got it right.) Remember the first time you kicked into Handstand? The fear of doing it can be debilitating, and whole lot worse than actually doing it. Rip the band-aid off fast and JUST DO IT.
Keep doing it. The more you practice anything, the less scary it seems. If you practice Handstand five times every day after a week or two, your hesitation will subside and you'll be able to kick up without even thinking about it.
Give yourself advice. Whenever I start to freak out about something, I think about what I'd tell a friend who was having the same problems. Most of the time my advice would be to take a deep breath and realize that it's not as big of a deal as it seems in the moment. (Then I think... Gosh, I'm a smart girl... wise beyond my years... )
How do you overcome your worst fears?