Beat all the challenges on hard. There are seven challenges you need to beat for this, and they will show a silver star jewel when completed.
Many hard challenges also come with a time limit. If you capture the required number of towns before the time runs out you win instantly. If you get to the end of the time limit and you have the most towns, you win. If you are tied on towns with another player it is a stalemate and doesn't count as a win.
So this part of the guide doesn't look cluttered, see below for more advice on beating the final hard challenge.