Use 8 light melee units; long range don't hurt them that much if they stand on bushes or forest, so study the terrain; the horsemen die quickly to light melee, same with the short range.
A strategy is to "lure" the cavalry first, by placing one or two light melee just in range for them to get attacked: I usually place my first unit in a place where only one cavalry attacks it, if cavalry strikes first, you'll counter and kill it when is your turn. Remember to take them down one by one, cavalry units counter once per turn. As you move towards the catapults, try to stay on bushes or forests unless you can land a hit or two; on some rare occasions -really rare- light melee destroy long range in one blow. Catapults deal extra damage if they stand on hills, so take down those first, same goes for archers on rocks (mounted archers count as short range, thus they can move on rocks unlike fast units).