Step on the catapult, and strike it to get thrown over the wall. You can try landing on the wall iteself to get rid of the pesky archer.
When you reach the entrance to the main building, it's blocked. The hidden entrance is found in the moat, by breaking the cracked bars and swimming through the entrance that leads to a broken wall. Once you're inside, you can search the upper floor for the mechanism to lower the drawbridge, allowing easy access in and out of the fortress. Also on the second floor just before the drawbridge mechanism is a marked wall. Striking it opens a secret door leading to a ballista which can knock down a tower to open a teleporter. Entering this teleport brings you to a ledge which has the mill key.
Return to Blackmarsh, and head to the Mill.
When you have the potion of mithril transformation, you can get the castle key.
In the room where you lowered the drawbridge, there's an adjacent room that has boiling oil pot. Look for a crack in the floor, and drop in. This will lead to a blocked-off section, guarded by archers. Ascend the stairs by pushing the barrel in the damaged staircase.
This leads to the skull wizard's room. There is a button hidden under the alcove's table, which opens a secret containing some bracers and a shortcut to the castle key door.
Open the windows, and jump into the water. Look for a mithril wall on the left. Transmute it, and break it open to get the castle key.
With the castle key, you can now enter the King's Court.