Well, since nobody is likely to know who you are at first..just act yourself and do a lot of observing, watch how the other "pros" act I guess. I wouldn't overtly cheer for any fighter but reacting to the action is human
I'm no writer, but this is just what I would do:
Prepare as much of the article as you can before the event even starts. There is plenty of background info for any given fight that can be done beforehand. that way all that should be left is the story of the fight and the play-by-play of noteworthy rounds.
Score every round, take simple notes during the fight. maybe voice notes so that you don't look down and miss anything. then summarize the play-by-play notes into meaningful paragraphs in between fights.
Think about a narrative that will open the article the day before and then one to conclude it with as you're sitting there. Sometimes there are 20-minute blocks of nothing happening at live events, so I imagine this is when many writers try to multitask and put in work. From what I've seen being at small to large fights, not all of them watch every single fight intently
I'm sure you've just sat back and had to pay attention to closely score a fight before, I would just approach it like that. Just prepare as much as possible beforehand and your stress level should decrease and most of your time can be spent paying close attention to the fights.