J.R.
It's so hard to be patient, especially when you're young, and I feel that our culture often glorifies the "overnight success" story way too much. There of course is no such thing.
Maybe plant some seeds so that she can see how gentle care and time are required before they bear fruit or flower. Read her stories of people who have become successful because of their hard work. I'm sure every biography of an Olympic athlete will mention how hard they have to work, how long they have to practice, and how much time the entire process takes.
I'd maybe try to de-emphasize "winning" when it comes to her goals and switch the focus to learning. Like "Let's see if we can film five minutes without the camera shaking!" Take a break from entering competitions, because clearly she's focusing more on the results than on the process.
If she does seem to thrive on a competitive atmosphere, maybe try to get her in team sports, so she also learns cooperation and patience. It strikes me that so much of what she is into right now is focused on individual glory, and it's easy to quit when it's only yourself you have to worry about.
I always hate to advocate video games, but there are a lot that require you to reach certain levels before you reach the ultimate goal of whatever it is.
Good luck.