Every year I have an outbreak of black algae even with perfect water chemistry. I now rely on shocking (>6ppm Cl) and shrubbing daily (as CarlD recommends) for a week with a wire brush to knock the slimmy protective "head" that forms and reduces the effectiveness of the Cl and copper algaecide. If a brush does not work, I use a pumice stone.

Once in awhile, I will add black algaecide that contains a couple of additional chemicals accompanying the elemental copper. Unfortunately, my spa becomes a bubble bath for a couple of days after.

Even when the black algae is dead, my spots do not immediately disappear, albeit they turn grey. More than one Leslie's Pool advisor has suggested I can rub a Cl tablet into the affected areas. But, my spots are usually near the bottom of the pool, so access is limited and Cl pool tips are hard to come buy(sic).

After a couple of weeks without new algae spots, I clean out my DE filter and recharge it.

Hopefully this helps.