Brushing is the only thing that works.

Yes, but you need the right brush and you need to be aggressive about it.

Black algae has a protective outer layer that pool chemicals alone struggle to penetrate. That’s where the brushing comes in — you want a stainless steel or wire brush, not the soft nylon one you use for regular cleaning. Scrub the walls hard enough to break that layer open, then hit the water with a heavy chlorine shock (like 2-3x your normal shock dose) and a dedicated black algae algaecide (usually copper-based). You’ll probably need to repeat the scrub-and-shock cycle three or four times over a week.

Vacuum to waste after each session, and keep your chlorine levels elevated for the duration. Black algae spreads fast — one missed patch will repopulate the whole wall.

You won’t win this with chemicals alone. Your elbow grease is the active ingredient.