To get this achievement, ride the train from New Orleans to Washington or New York. While on the train, you'll converse a bit with a boxer named Sullivan. Mister Fogg will make a bet and encourage you to get into a boxing match with Sullivan on the train; you can refuse, but it is best to accept and try and win the fight.
It is fairly simple; you get advice from Mister Fogg during the fight, and can also observe Sullivan while boxing. You want to block when it looks like he's going to punch you as hard as he can, and you want to punch him with a hard punch when he is looking like he's going for a weaker punch. Fogg will tell you when to hit him a few times, and you'll want to follow his advice.
Otherwise, just do your best. If you win, you not only win a sizable amount of money, but also the achievement.