I'm pretty sure that is a Cassiopeiea spp. jellyfish. It looks like it's dying already. These animals are actually fairly easy to keep in dedicated setups.
From what I understand these jellies come from brackish to full strength salinity waters, in areas of fairly high nutrients and plankton density. Water quality and stability aren't so much of an issue with them. They do need to be fed small planktonic type foods, and lit with intense light. It won't catch your fish.
We had some in the following setup a while back--
20 gallon tank, 6500K 250W MH. NO live rock or any hard substrate. Southdown or very fine sand. A reverse flow undergravel filter with a powerhead pushing water up through the sand. Very, very light flow, I think the powerhead pumped 100 gph or so. The powerhead had a foam filter on it. That was about it. We fed cyclopeeze and phytoplankton every other day, and topped off the tank weekly or so. They reproduced at one point and released planula larvae that settled onto decaying mangrove leaves. I didn't make a concerted effort to raise the polyps.
If you'd like to get more info, you should contact Chris (aka Grendel) at this site. He is very familiar with them. And in the future, do this type of research before you buy!