Also, keep up the superchlorination, even though you may have killed all
the algae. It takes days, but chlorine will oxidize the dead algae
clouding your water into gases that outgas thorugh the surface, or soluble
inorganics that don't cloud the water. Anything oxidized is that much less
that has to be filtered, and you can oxidize almost all of it if you
superchlorinate long enough.

Don't use cyanurated chlorine to superchlorinate (and check that you don't
already have a build-up of cyanurate, cyanuric "stabilizers" spoil
chlorine's sanitizing power to where it won't clean up algae). Use sodium
or calcium hypochlorite instead of cyanurics.

Keep pH low, way below swimming comfort until you finish the cleanup, this
will get much more power out of the chlorine and deter any new algae
growth. Match each chlorine dose with the acid needed to overcome the huge
alkalinity baggage that comes in the chlorinator liquid or powder.

Dose chlorine at dusk.