tap water is a big problem, and you probably won't be rid of this algae until you stop using tap water.
you need to get phosphates down to zero. you can use phosphate pads and/or PhosGuard (or similar products), but again, you are probably not going to get phosphates down until you stop using tap water.
when you've stopped using tap water, start picking the stuff out by hand as often as possible. each time you pinch some out, dip your hand (with the algae) into a cup of cold tap water (to keeps any algae from getting back into the aquarium when you put your hand back in).
get as many pencil urchins as you can afford. they are only about $6 each and they will mow through hair algae (and coralline too, unfortunately). fish and inverts generally won't eat hair algae if it is thick and bushy like yours appears to be.
it will probably take a month or two, but I believe this will solve your problem. believe it or not, I had a hair algae problem worse than yours. I did the above, and the problem's almost solved.
I also did all of this......cut feeding down, cut light down, increased water flow. none of this worked, but getting the phosphates down, using RO water, and using Pencil Urchins will help.