Near the end of the Black Book, at the top of Minas Morgul, you will reach 14.2 Gothmog's Rage, which is a quest instance. It took me 6 tries to complete it. Being defeated sent me back to the bottom of Minas Morgul, requiring another run back up the levels. Very annoying. Here's what I finally figured out:
After some drama outside, you go in and confront Gothmog. The fight was not hard: first, 3 mobs in sequence, then the same all at once. Culang helps.
Then you fight Gothmog. You get a huge buff (damage and mitigations), so that fight is not hard either. The problem comes next.
It turns out you did not defeat Gothmog, he has been toying with you. He begins a sequence where circles appear on the floor and burst into flame (46k damage to me). You need to dodge the circles (no fighting). After a while, a set of NPCs appears with quest rings. You will need to click on them (you have to stand still for the induction). If you survive dodging the damage circles and click on all the NPCs, you win.
It turns out the damage circles are not random, but are essentially a checkerboard that alternates with the damage circles on the black squares then the white squares. I strafed left and right with the Q and E keys. Don't wait for the circle to appear before moving. As soon as the flame disappeared, I started moving to the spot where it had been.
The NPCs appeared in a row behind where I had been at the end of the previous fight. Once I realized that fact, I moved back before Gothmog started the circles so the NPCs were in front of me. It helped to zoom out a little.
Once you've done the last NPC, the circles stop and it's over.
After that was completed, I still managed to die doing the next chapter, falling through a gap in the floor I didn't notice, but I didn't have to redo the hard part.
If you find an easier way to beat this, let me know. I'll have to do it 3 more times.