To be honest with you, I don't know if you'll be able to completely change your accent so that you sound exactly like a native speaker. And SteveMP is right. There are many accents in the U.S. Someone from Texas doesn't sound like a person from New York, and so on. I think that the Midwestern or Western accent (Washington, Oregon, California) are very standard and are the ones you should go for. Southern accents (Texas, Louisiana, Georgia, to name a few southern states) are often made fun of, and so are East Coast accents. And those will sound especially weird coming from a foreigner. I would say that the Midwestern/Western accent are the most common and acceptable ones, and I've found that sometimes even people who aren't from the Midwest or West of the country often have one. Again, I don't know if you will ever be able to not sound Russian when speaking English, but I'll say that really it doesn't matter because don't worry, a lot of people do like Russian accents and find them to be charming.

@SteveMP I don't know about this topic I just wanna speak like American girl :)

There are TONS of accents. Which one are you trying for?

I can help you if you don't mind.