Edit: The links now work!
For most players, all Mafia Wars Moscow boss fights are mistakenly locked, effectively blocking these players from advancing to the next level. I had posted up some links a few months ago, but these have since become outdated due to a recent game changes. Thanks to Scott (of egg oddity fame), who tipped me off about this change.
For the highest chance of success, you should be logged into Facebook and be in Moscow. Then, right click on the boss fight that you want and click "open in new window". If you try to copy and paste into a new browser window, for some reason this will not work. Make sure you give the game enough time to load so that the help box will pop up.