If I'm fighting a big fish, I try as best as possible to stay parallel with the fish along the river. Its super important that you don't let the fish get downstream of you if you can help it, and if its a little upstream, that's not always bad either. This gives you the upper hand in that the fish has to work much harder because he's battling both you and the current. This will exhaust the fish much quicker, and in reality you want to be fighting these fish for as little time as possible. The longer the fight, the higher chance the variables will come into play and you lose the fish. He gets downstream of you, you're in a world of trouble, as you have to go catch up with him, and in that time, you need to worry about obstacles in the stream, slack, etc.
I also try to get them on the reel as fast as possible. Sometimes these fish will immediately come at you right after setting the hook, and I see a lot of people make the mistake of trying to "reel it in," when there is way too much slack in the line for that to be effective. Usually this results in the fish coming unhooked when they finally have the slack in control. If the fish starts coming at me, I strip in line as fast as I possibly can, when he settles for a quick second I reel in the slack and try to get him back on the reel.
It is also important to be aware of major obstacles in the river, such as big boulders, rapids, to help you avoid taking the fish or letting it take you into them. Sometimes you can coax the fish around them if you're careful with the line tension and keep your rod tip high, and play the angles.
... just a few things I've learned over the years through trial, and mostly error :![]()