Complete the first 5 order missions. It doesn't matter what medal you have for each of them, as long as you complete them.
I suggest trying to use KChess if you're getting stuck, but this will probably not help you regarding gold medals.
It's impossible to say how to complete each task because it's reliant on what the computer does, and every time you play, the computer does something different, so it's impossible to guide you through each mission.