Ok, so this was one hell of a mission. No matter what I tried I got slaughtered. The problem was that the enemy archers and crossbow men were having a field day wasting my troops until I got anywhere near to taking them out, especially since my only units capable of taking them out before I breach the gatehouse, ie my ranged units, are high priority targets. After briefly trying to attack from the left and right and each time getting slaughtered I gave in and sought out a walkthrough for the mission. Problem is, the only guides I could find for the mission were for the original version for the game, where it was possible to take out most of the archers and crossbowmen on the towers without taking any casualties. Unfortunately (or fortunately) that does not appear to work in the HD version.
Following is how I managed to beat the mission, on hard, with the majority of my forces intact, and with a lot of time to spare. If there are other perhaps better strategies please be so kind as to let me know.
The basic idea of this strategy is to get almost all of your archers and crossbowmen into one specific tower in the castle. Once they are in that tower, you've essentially won.
1.) I find it useful to press spacebar to remove all elevation for this part. Move all of your forces to the top right of the map, except for your archers, crossbowmen, battering ram and 2/3 melee units, making sure that they don't walk into the firing range of any of the enemy archers/crossbowmen. Leave your archers and 2/3 melee units near the battering ram to deal with the enemy macemen that will come out to attack it. Move your crossbowmen to the little rocky hill close to your starting position. You have to be incredibly careful here: There is a sweet spot from which your crossbowmen can fire on the southeast tower from where they are safe. Arrange your crossbowmen in a line along that point and take out the first crossbowman on the southeast tower. The other crossbowmen are 1/2 tiles further away so you'll have to advance your line of crossbowmen 1/2 tiles ahead to kill the remainder of the crossbowmen on the tower. If you do this right, then none of the enemy crossbowmen will fire back at you. The moment you move a crossbowman too far forward you'll know about it because an enemy crossbowman will advance to the edge of the tower and start firing at you. The only other thing to note here is that archers will periodically run up the tower to occupy the position of a slain crossbowman, and might even move to attack you. That is not a problem though since they do little damage to crossbowmen and you can quickly take him out before you continue attacking the other crossbowmen on the tower.
2.) Next you have to take out the archers on the tower in the inner courtyard just north of the tower (up and left) you cleared in step 1.) Unfortunately here you can't attack the archers without taking return fire, so to minimize casualties use both your archers and crossbowmen together to quickly clear the tower. On sh2.jpg I have my crossbowmen in a pretty good position to attack the tower, and I had my archers positioned just above them.
3.) Now, as soon as you move to attack the tower in step 2.) send 6/7 macemen to fill the moat at the base of the tower you are attacking. The archers that are firing on your crossbowmen and archers will ignore them since they are lower priority targets. The moat filling AI is a bit wacky so you'll have to babysit them to make sure that they only fill in the moat in the direction of the tower. At some point you'll notice that the macemen have filled in enough of the moat that they can attack the wall near the tower. Let them attack the wall and wait for them to make a breach. Due to their position at that point they will be safe from archer fire until they've made a breach in the wall.
4.) The hardest part is over! Send all of or your remaining units into the castle! All of your crossbow men and all, or almost all, of your archers should be alive at this point, so now send them into the tower you cleared in step 2.).
Send your other forces to clear the the other towers in the inner courtyard. Specifically, send 5 or so macemen to clear the tower on the other side of the wall breach, and send the rest of your macemen to clear the towers separating the inner and outer courtyard that are filled with crossbowmen. I used the spearmen to clear the remainder of the courtyard, along with the other two big towers along the west wall.
5.) Let your archers and crossbowmen do their thing! Use some of your macemen to destroy the gatehouse separating the two courtyards if you want to speed things along. Before long you'll have cleared the entire castle with minimal casualties and time left on the clock.
I hope that someone finds this approach useful :P
