How can one get rid of Russian accent?

I know it very well, that speaking a perfect (either British or American) English is extremely hard to achieve. Moreover, trying to imitate a certain accent may sound like pretending someone who you are not. But nevertheless, I would like to get rid of my Slavonic accent, or at least make it a bit more subtle. The reason for me making such a decision is the image of my home country. Tell me, please, what comes first on your mind when you think of Russia? Bears and vodka? Or is it communism and the Cold War? Whatever associations you have, I guess they are not very pleasant.

Back to my accent, I would like to know what sounds I should work on, is my intonation correct or not, and so on and so forth. Any help will be appreciated as we’re all here to learn English.

Waiting for your comments,

Hey Galya,

I’ve listened to your recording,

Even though I also have obvious accent, I pay attention to the subtle details of accents.

You have some cool English accent in some of your words. Some people might almost mistake you for a native speaker.

When you said ‘when you think of russia’, it sounded Russian but it wasn’t thick. Also, when you said ‘they are not very pleasant.’ it also had some Russian intonation to it.

I guess the main reason why people don’t want to have an accent is because it may not sound as sophisticated as native accents in some ways.