Sorry I missed this when it was first posted, but hopefully an answer even now will help others searching for help, although it may be too late for the original poster.
This is Dictyota algae, which is an annoying and frustrating algae to deal with. It's toxic and the only known grazers are Naso Tangs and Double-Barred Rabbitfish (Siganus virgatus), but unless you've got a large tank, neither are good options (borrowing one temporarily from someone with a larger tank may not solve the issue, as they will graze the Dictyota down, but once removed, it will grow back). Hermits and snails won't touch it. It reproduces by fragmentation, so manual removal always risks spreading it still further, as small pieces that are not taken out, either by siphoning or hand, will then settle and grow elsewhere in the tank. If you do plan to fight this manually, it is best to try and do so out of the tank (I'm doing so at the moment by saving a bucket of tank water when I carry out a water change and using that). You will have to scrape it off, probably removing coralline in the process, as leaving small amounts stuck to the rock means you're only pruning it.
Unfortunately, it thrives in low nutrient, high light conditions (as well as high nutrient, low light), so simply cutting nutrients isn't guaranteed to solve the problem.
I'm about to embark on a course of treatment using Algaefix, a product available from LFS and online stores, which some people have had success defeating Dictyota with. I'll report back once I start (it's on order, won't be here for a couple of weeks). Meanwhile I'm removing obvious patches of the stuff to keep it manageable. Without doing so, it rapidly overgrows corals etc.
There are spiders that can live around the water, but they are freshwater only (afaik) and they live outside in the air, they just capture air along their hairs to breath while underneath for short periods.