This is a temporary solution for those who have the free version of the game and can only play game of the week. I am unsure when this started so it may not be on much longer. As of today 06/05/14 there is a derby game in game of the week.
if you go to home and update squads you should be able to also download news game of the week matches. One of them is ac Milan vs inter milan. Play it and win. Should unlock at the end. I won 2-0 with AC.
Without the full version this seems to be the only way to obtain this achievement. But the good new is that it only puts high profile games in game of the week so there should be at least one derby often. Il leave the solution up and will keep an eye and update when there is a derby that week. Feel free to let me know if a new derby comes up yourselves in the comments and Il update my solution.
Current Derby on Game of the Week - Portland Vs Sounders FC