A two-stage battle
My strategy for fighting a catfish from the shore is as follows. Once the fish is hooked, it will try to go upstream, certainly by instinct because they all do that. So I let the fish try to go upstream, reel brake tight but not completely. Thus, I want the catfish to exhaust itself by letting it take a little bit of line with difficulty. I try to bring him closer to me if possible but above all, I let him do it which avoids me to be exhausted before the second phase of the fight which is much more intense.
At some point, the catfish will turn around and go downstream, this is the critical moment when everything is decided. Often, it is complicated to follow far the fish because of the crowded banks. The principle is to "block" the reel so that the fish, combined with the force of the current, makes an arc and is drawn towards the edge where I can catch it by hand. This second phase is very critical for the material, hence the need for it to be proportionate. If the fish ever gets too far into the current and gets farther than you can follow it, the game may be over quickly because it will not move upstream as long as it feels pressure on it.

A second chance
If the catfish goes further down than you can go, the solution, instead of breaking, is to open the reel pickup and see what the fish does. Luckily, if he doesn't feel any resistance, he may start to swim back towards you. So there is nothing to lose by trying this trick and letting the fish go as far as possible to "fight" it a second time.