Black algae needs a wire brush and bleach.
Yes, it’s tough, but not immortal. Black algae in pools is a cyanobacteria that grows a waxy protective layer, so normal chlorine levels just glance off it. It usually shows up when chlorine is low, pH is high, or there’s a dead spot in circulation.
Treatment is brute force: brush the hell out of it with a stiff wire brush (not nylon) to break that coating. Then shock with three times the normal chlorine amount, keep the pump running, and lower pH to 7.2. Hit it with a pool algaecide. Repeat the brushing every day for a week. If it’s really stubborn, you can use a copper-based algaecide, but don’t overdo it—copper stains.
Prevention is easier: keep chlorine steady, brush weekly, and run the pump long enough to turn over the water. Black algae loves neglect.
Future you deserves a pool that doesn’t look like a science experiment.