In this case my advice would be to get in touch with the Irish Embassy in Moscow
for more information about a visa for the Republic of Ireland and Northern Ireland. They will be able to tell you exactly what you need for your trip.
Even though there is no border when you travel between the Republic of Ireland and Northern Ireland, sometimes there is border patrol checking identification. There is something called the British Irish Visa Scheme
, but at the moment this is not available for Russian visitors. The Embassy can advise you on what to do in this case.
Hope this helps, and let us know if you need some tips for your visit!