My guild has been steadily working working on the Lich King encounter on 25-player mode for several weeks now. We've managed to gradually chip away and gain some meaningful progress on the Defile and Twin Val'kyr phase. If it were just Defile, it wouldn't be a problem. Likewise, if there were only Val'kyr to worry about, we'd ace it easily. But combined, they present quite the interesting challenge. It isn't exactly the most enjoyable part of the encounter for me as a healer. After taking him down in the 10s, I can say the phase where all the spirits are flying around and waiting to explode on some player is enough to keep me on my toes, as well. The last boss I remember really holding my breath on would be the final phase when tackling Yogg-Saron. I suppose my best theory on that would be the longer I've worked on a boss, the more tense and focused I would get.
There was one specific phase during the Illidan fight that kept me on my toes. The veterans of the game might remember the second phase where Illidan took to the air and impaled his war glaives on the ground, which summoned two fire elementals. They had to be tanked at a certain distance and a certain angle; otherwise, the elementals would completely fry the raid.
Archimonde had the same effect on me. Can you guess which part? It was when players were thrown in the air and had to rely on Tears of the Goddess to safely land. I cheated and Levitated.
A more recent encounter would have been Sindragosa. Every time she pulls players towards her and lights up an explosion, I get a little uptight. Someone seems to get hit.
What about you? Which parts of a fight cause your back to straighten and your fingers to hold that mouse with a firmer grip?