You'll need to have conquered the Seregost fortress to trigger this mission, as Ringwraith Helm Hammerhand launches an attack to take it away from you. The mission description makes it sound like this is going be a siege defense, but it isn't quite. Still, it does start with an any force outside your gates. As ever, take the battle straight to them, blowing up the grog barrels on the battlefield.
Once you're on the ground again, ignore everything but Helm. He's a little different than the standard Nazgul- for one, he'll pull you to him for an attack, rather than teleporting over.
Also, his hammer attack is a relentless series of swings, rather than a single strike, so you're better off just rolling out of the way entirely while he rages. Still, the basic strategy of focusing on the nazgul and making counterattacks remains sound- keep up until he mutters his threats and teleports deeper inside the castle.
There are no points for him to conquer, so let him putter around while you take down a few more immediate threats, like the drakes.
Once you've cleared away the major hostiles, go after Helm. His new trick is summoning mobs of ghuls.
Ghuls are easy to kill, but can't be parried, so do spent a few sword-swings or grog-explosions to clear them out before re-applying standard tactics to Helm.
As before he'll peace out after losing another chunk of health, and as before you should stick around to deal with the local threats before chasing him. In this case, the giant tundra graug.
Kill or dominate it, then chase after Helm again. This is your last encounter with him, so you're going for all his remaining health. One tip is that Banishing doesn't seem to phase him much when he's in his hammer rage- wait for him to putter to a halt before putting the whammy on him.
There'll be a brief fakeout where it looks like he's going to kill you, then Eltariel steps in and saves the day. This little bit of NPC heroics completes the mission.