I try to stay away from doing dialogue in serious and/or extreme situations simply because I don't want it to kill the mood and I'm too afraid of it coming across as corny or something. Not that you can't do it at all, but it's something that I try to keep only as heavy descriptions with minimal dialogue if I can.
You could surround dialogue by sliding it in around the actions of that character but be careful not to break any story flow. I stay away from it because it's kind of tricky to do. Especially for me since I mainly write romance, not action.
If it is an extreme emotional scene, I tend to add more inner dialogue than anything said out loud. Feelings and emotions too. Like, a pain in someone's gut or a warm feeling engulfing their body from embarrassment. Things like that. If you want to add dialogue, you can always add inner thoughts of them taking note of how they feel as well, or them speaking in a certain way. Use words that help give the correct atmosphere to the air, like if two people are very close to one another they speak in breathless whispers.
I fear I'm a strong romance writer, so that's my first example.
Fighting scenes, you can use things like scratchy throats, raspy tones, prideful voices, etc. Just use connection and describing words that fit the context of the situation, and it should be all good.