The first level of the Mongol campaign is impossible on hard. Has anyone passed it? Even when doing everything seemingly right, my army gets destroyed with half of the enemy still alive.
Group your Mangudai with the Khan, when they tell you to go pull the enemy’s army into the ambush make sure to kite them with the group of Mangudai + Khan all the way back, you can clear 30% of them before they even reach the ambush site (use the fire rate bonus). You don’t have to place any melee units on the front of the ambush site, just keep kiting the spearmen force across the river with the Mangudai and collapse on the archers at the back with everything else.
If you want to spend a lot of time you can probably kill all melee units with the mangudai as they aggro before the ranged units but go back to the river afterwards. If you’re willing to spend that time you’ll have all your melee riders for the ranged units.
Otherwise just be careful that your lancers and horsemen properly engange the archers from the back.