Like many Punch-Out!! opponents, Vodka Drunkenski can be very tough if you don't know the trick, and very easy if you do. This big guy doesn't have any real special moves, he's just strong and aggressive. That aggression is going to be his downfall. Keep your guard up, covering your face, as he will usually lead with a jab. His two main attacks in the beginning are a jab and a hook, and two jabs and a hook. Do not lead into him, he will counter it. It's not necessary to, anyway, because he will throw plenty of punches of his own. Block the jabs, dodge the hooks, and jab back. If his hook places him to your right, hit him with a right, and if it places him to your left, hit him with a left. (If you hit him with a right when he's on your left, it will connect but you won't get to follow through with more jabs. Be careful!) Then continue with left jabs. Eventually he will start using uppercuts -- you can tell when he enters this phase when he throws a jab but doesn't follow it up -- and those are easy to dodge and counter, too.
If you knock him down, his first move when he gets back up will always be an uppercut. Dodge and counter as usual. That is all you need to know to bring down Vodka Drunkenski.