Your first move will be the same for almost any siege- leap over the wall and use bird of prey to break the nearest siege beast, shadow dominate it, and then use it to blast the other beast, or blast the nearby captains, and then shadow dominate the other beast as well. Do NOT try to take out the enemy troops clustered at the gate- you'll only wind up damaging or destroying your own defenses.
When your feet are back on the ground, summon a drake or graug to harry the enemy army, but don't summon followers just yet- you'll want to keep them in reserve for any warchief duels that turn dire.
You'll also want to clear away enemy graugs or drakes at this time. Your next objective (and really your only other objective) is take out the enemy captains. Refill your arrows with Quiver of Souls if you need to, then see which captains you can tag at the wall. If you don't have spiked walls yet, prioritize climbers, particularly caragor riders (as opposed to ologs, who can't climb at all). Soften them up with a headshot or two, then Shadow Strike in for more traditional combat. The key for this is speed- use your fastest tactics to take these guys down. If a captain has a set of immunities that prevents this (an arrowproof, stunproof, frostproof vault-breaker, for example), move on to easier prey. You can come back for him when the rest of the rest of his buddies have been rendered harmless. You can also buy time by using Freeze Pin and fly nests on the heavies you're not currently engaging- both keeping them from their objectives and making them easier targets for your allies.
Continue to hunt down captains- remember that taking out the assault leaders is the only win condition here- defending points and keeping your own people alive can be helpful, but it won't complete the mission. That said, defend points when you can. This isn't too hard to do, because a point that needs defending is usually a point with a captain (or captains) that need killing. Also, if a point falls, another surge of enemy forces will Kool-Aid Man through the nearest wall, cluttering your battlefield with a new assault leader, extra ologs and other unimportant-but-tedious-to-kill invaders.
The last rule is simple- look out for number one. While many things can shift the tide of battle this way or that, your death is an automatic fail. No matter how caught up you get in slaughtering the enemy, remember to keep an eye on your health, and fall back if you're seriously threatened. Better a captain die covering your retreat, or even a point lost while you recover focus, than to lose the fortress entire.
With these tips, dominion over Mordor is as good as yours.