Start by going to the Olympic Games and enter Olympic Mode. Select the Romanophone event on Medium difficulty. Follow along through the tutorials until you get to the actual event.
The way this works is that you and your opponent will both be on a platform with different colored Roman soldiers. You must hit the colored soldiers in the same order as the colored notes at the top of your screen. Complete all of your notes before your opponent to win.
This event can be a bit frustrating, so here are some tips to help you out:
Remember that the Red soldier will always be in the center of the platform. The Yellow, Green, and Blue soldiers will travel clockwise around the outside of the platform and stop briefly at the corners.
If you are having trouble reaching the soldiers before your opponent does, try using the "B" button to slide into them instead of running over and pressing "X" to hit them.
There's not much else I can tell you for this one. Just memorize the pattern, and be fast.