Kuda,
Has your pH changed at all? IME hair algae seems to like lower pH's. If it were me, and it has been (a few times), I would:
Hand pick out all the algae I could. If you can remove the rocks and place them in a bucket to help scrub them without getting stuff all over the rocks great, if now then do it in the tank. Just pull out all the algae you can. It might take a couple hours, but it's worth it.
Then do a big water change, using the siphon hose to vacuum the rocks and all the nooks and crannies. Sometimes using a power head to blow stuff off or out is helpful if you don't have really high flow in your tank.
Then kill the lights for three days. Keep the skimmer going, it might go a little nutty, and run a UV if you have one. The no light will help to kill some algae and help all that stuff that got away when pruning just die. When the algae dies it will be releasing some of it's nutrients and spores back into the tank, hence the crazy skimmer and the bonus on the UV.
Then do another large water change to help remove all the extra nutrients that are still in the system that the algae released. Dot he same vacuuming process again too.
That itself won't win the war, but it's a good opening attack. Not sure what fish/ CUC you have. or what's on your wish list, but now is a good time to start adding a herbivorous fish if it's on your list, increasing the algae eating snails, and or hermit or emerald crabs.
You can beat it, it just takes time and diligence.
On the cyano issue, after I have "fixed the problem" the cyano has never gone away on it's on. The 3 days no light did kill it and have it never return though. It's a pretty resilient bacteria so if there is food for it, it will grow. JMO