You'll have to pay 5000 gold at the entrance to get inside. Once you do, you can talk to the man you meet to learn that you're trapped in a haunted destination. From what I can tell, this area serves as an Easter egg of sorts, acknowledging people who contributed to the Shovel Knight campaign on Kickstarter, back before the game was funded.
Climb the ladder along the top of the room to reach an overhead chamber. From here, you can head in a few directions. Start by traveling left. As you go, collect gems and watch specters materialize behind you. Climb a ladder, then hit the wall to the left to reveal an opening. Pass through it and you'll find a high ledge with a chest. You can open it for gems, and also you should grab the Music Sheet
that hangs in the air above it. Note that there is a pitfall near the left side of each statue base, but you can hop across those easily enough.
Head back right and proceed in that direction. The glowing orbs can be hit with your shovel to launch them a short distance, including onto floating ledges. If you launch them toward specters, they'll defeat those enemies for you. Then you can head right to reach a room with two more waiting pedestrians, and a picture window behind them.
If you head down the ladder, you're back at the initial fork in the path. This time, go to the right. You will reach a stone column, but you can jump up and hack it to produce an opening. Pass through that opening and continue right to find another of the glowing orbs. Use it to eliminate any nearby ghosts. Then hop on the lift and ride it up a short distance along the stone column. Hack at the column to produce another opening.
Continue through that opening and use the orb to destroy another nearby specter. Light will likely flood the area, assuming you've eliminated all of the nearby specters. Now climb the ladder just to the right and you'll arrive in a room with a few more specters. The ladder leads to an upper ledge here, which has a few pitfalls, every other block of bricks or so. Knock the orb around this area to eliminate the two nearby specters, and proceed left to take out another specter. That should also light this area. Now you can head left again to return to the room where the people are positioned in front of the picture window.
Travel back left through an unlit room, and down some stairs into another with a bunch of dim portraits. From the ladder, head down to the floor level and knock the wall to your left to reveal an opening with an orb. Now, you can knock the orb to the right and proceed that way to tend to some more specters, finally lighting up the room in the process. Then climb back up the ladder to the room overhead.
Head back toward the right, near the floating ledge. You can chop at that wall to reveal an opening. Keep revealing more openings, and you'll also find a specter's hiding place. Defeat it with the nearby orb and you should bring light to this room, as well. Now return to the room where people were standing in front of the picture window, to the right.
The ghost is a bigger version of the specters you have dealt with throughout this area. He starts by swooping slowly around, out of range. You should notice two orbs along the floor. You can knock those around to deal damage, as usual. I like to line them up so that a single swipe makes them both go flying in the same direction, but I'm not sure that actually helps. It just works well for me.
The ghost uses a few attacks as the battle wages on. He likes to circle the room, which is a great time to knock the orb against him, but you ned to be careful not to let him run into you along the way. He also will sometimes summon a ring of ghosts, or make clones of himself, or he'll fire little skulls. No matter what he's doing, you should continue kicking the orbs around, because those are your only way to do any damage. As long as you keep doing damage to your foe, it's an easy fight. Use your pendant to avoid taking damage sometimes if you need to, but even though should be a totally optional step if you hustle properly.
The ghost yields 6000 gold when defeated, so at least you come out ahead. After the battle, you will talk to the woman back at the front gate and she will also pay you a small fee, besides awarding you the "Hall Champion" feat. Exit to the world map.