You can check with banks or immigration bodies if they could verify the Russian birth certificate translation. As a rule, they can do this free of charge. I also heard, that there were some cases when they charged 20 USD for this service.
When verifying the Russian birth certificate translation, it is very important to write the following on the certificate:
I, (name), certify that I am fluent in Russian and English languages and that the above/attached document is an accurate translation of the entitled Birth Certificate.
(address of the person who verifies, telephone and signature)