Winning the African Cup is quite easy. It is an 8-team single elimination tournament. You only need to win 3 games. Use the lowest difficulty allowable to unlock the achievement (regular), the lowest time limit (3 minutes), and obviously pick a strong team (I chose Cote D'Ivoire).
Before you begin, randomize the teams in the tournament in your favor. Also, do not forget to put Drogba in the line-up, as he is on the substitutes list.
Personally I like offensive minded football (soccer), so I used a 3-2-5 formation. I also played on the hardest difficulty (Top Player) in order to accumulate wins for the "Legend" achievement.
mydefposse has 2 great tips in his solution for
1) When the opposing team's keeper has the ball, move your closest player to him. As he is about to kick the ball, run towards him and you will have the ball at your feet with an open net to shoot for.
2) If you're about to lose the game, hit the Start button, wait a few seconds, hit the Back button, and the game will reload and you can play the match again.