I use to place my units by a ford or bridge. Place some pikemen in a semicircle around the bridge, and plenty of archers behind. You also need 4 formations of heavy cavalry for the countershock as well as some assortment of catapults and ballistas. As soon as the Mongols begin to cross the ford/bridge, you place all artillery barrages at "Fire at will" (make sure the fire lanes do not allow for friendly fire). Also, use "fireballs" for the catapults, as that generates mass death on that narrow bridge/ford. as soon as the first group of Mongols (most likely mounted ones) reach your pikemen, you start firing with archers on the troops in the middle of the bridge. As soon as the Mongols have crossed the bridge, you stop the artillery for a little bit, do the strong counter on their flanks (our side of the river) and crush them there, just be wary of enemy spearmen/ or pikemen.
Then you retreat your cavalry, then hammer again, then retreat and hammer again. When they begin to panic, you send everything you got, as you fire with artillery and archers. As soon as your troops are halfways, you attack them with archers using unsheathed swords (ALT function and mouse).
Then, you bring all you got, in particular you General, as his free kills builds character. This game does not really differentiate between slaughtering panicking soldiers than bravely winning an intense swordfight, like real life.