I am trying to beat the Mad Russian, when I kill him he just comes back…

You don't!!
He's supposed to join your quest and together, you go after Mr. White or Mr. Wong. After you killed him the first time, He's supposed to talk to you. Does he have the white bubble over his head with the "!" in it? If not, you may have a glitch in your game and will need to go back to an earlier saved game.
Sorry!