I'd make one adjustment to BigDave's advice.

FIRST, bring your pH down to about 7.2/7.3, or even as low as 7.0, then measure your T/A again. Dropping pH from 8 to the low 7's should bring down the T/A as well.

Your target shock level for your CYA level, is 20ppm, but, personally, with black algae on a hard-sided pool, I'd go to much higher levels, as high as 40ppm, to kill that junk. But that's me.