Hey Juzzrach! I think the easiest way is to take the Business Bay crossing fro Al Khail. There are lots of signs to Al Badia but the easiest is to take the Festival City exit and head down past Ikea and the mall (on your right) and Ace (on your left). If you keep going on this road it will take you straight into Al Badia.
HTH!
You can always call me if you need more directions or get lost ...