Here's a very fun battle against TWO stacks of Mongols.
As you can see in the screenshot below, I've repositioned my troops on a huge hill, and the opposing Mongol army (Mongol army #1) likewise repositioned on the opposite hill. When the AI is on a hill, it is very stubborn. The worst thing to do is to attack an elite army with lots of archers positioned on a hill, and backed by lots of cavalry that would crush anything you send up against them. Without a full stack of chivalric knights, attacking that hill directly would have been a bad idea.
Fortunately, the second Mongol army arrived from the left side of the image. Instead of sneaking to the top of the far hill right away, they marched though part of the canyon-like valley in the middle. As a result, my archers (the entire army basically) opened fire. When the AI is under heavy archery fire, they will always attack you, even if they must give up the high ground. So here, since Mongol army #2 was under heavy fire, Mongol army #1 abandoned its high ground and moved into the valley to attack me uphill.
I held the ground and won (results in second pic). In this battle, I had a general with 10 chivalry (max chivalry) and 9 command stars.