Here's a few things I have learned in my fight against Green Hair Algae and other algae.
Myths
Reducing lighting will kill off the algae: Algae DOES NOT need any light at all to survive. Yes, it needs it to grow, but once its there it will live on (forever?) with no lighting at all.
Proof: I moved the worst of my algae covered rocks to a Bruute garbage can full of new salt water. A heater, circ pump and airstone were put in and the lid was put on. After at least 3 months (I think) when I pulled some rocks from the bottom out, they were still covered in a bright green hair algae. Complete darkness did absolutely NOTHING in the way of killing off the algae.
Getting your nutrient levels to 0 will kill of the algae: HA! biggest joke out there. Sure higher levels will PROMOTE algae growth, but it seems to grow just fine in a system with amm, 'trites, trates AND Phosphates all at 0. Yes, the test kits and hanna checker are all fine.
Proof: Not only are my readings all at 0, my phosguard has shown NO colour change after 8 months. And my skimmer was more like a fizzy, um, thing, again indicating there were no long string proteins in the water.
What is my GHA using to grow, I'm not certain, but I'm having a heck of a time keeping my alk levels up. Perhaps GHA can grow using some type of carbonates. IDK. But both the GHA and Chaeto did just fine growing with nitrate and phosphate at 0.
Things that worked, somewhat
Dosing with Hydrogen Peroxide (H2O2) will kill algae (and other stuff): No, simply dosing with it wont do anything to anything. However targeted applications of H2O2 will kill algae. I used 25-40 ml in a 110 gal + sump system.
H2O2 dipping: This worked to kill algae. I dipped some corals (LPS and shroom covered rocks) that seemed happy for the treatment. I read that SPS can't handle the dip, so I didn't try.
Problem: I can only get 500ml bottles of 3% solution. That is the strength I used, but 2 bottles was needed for some dips. H2O2 turns into plain water very soon after pouring it out of its container, so you can't save it for tomorrows dip. I think you can get 25% H2O2, but not where I live. If I could I would have used a 5 gal bucket 1/2 full with RODI and then mixed the H2O2 to a 3-4% solution and dipped all algae rocks and my hammers too (too big for me now).
That's it.