Pick your team that you'll bring inside the Palace and enter it the same way as before, crawling through the vent after jumping across the top. When you jump down into the area with the elevator, you will need to watch out for some enemies. One will be right by where you drop down and there will be two others on the other side of the room. You will want to enter the door on the other side of the room, opposite of the chest you opened on the previous visit, which will bring you to the backroom area.
Tip: Remember to always cover for the elements your current team doesn't have. For example, if you bring along Makoto, Ann and Yusuke, then you want electric, wind, psy, bless and curse skills on your Personas.
Go through the first door and the dead end nearby, as well as the next door you come across, will lead to just breakables. Follow the hallway until you go down some stairs, where you will come to a split. Head east first and you will eventually reach a dead end with a chest, containing a Heaven Ring . Return to the split and head west now, going south across the machinery and keep going south until you spot two doors. The one slightly off to the west is locked and requires a keycard, while the other one just has a breakable.
Continue north, past the locked door, to spot another door that leads to a treasure chest with some Seedy Gear in it. Past that are some stairs with a menacingly looking guard at the top, but ignore him for now to find a Safe Room at the far north. Attempt to go up the stairs and your party will give you an option to either confront the guard head-on, or find another way around. If you use your Third Eye by the safe room, you should notice that you can climb on top of the machinery, where you'll find a vent.
Crawl through it to appear in the area behind the door the Shadow was guarding. Go through that door to fight that same guard with an ambush initiative, which turns out to be two Midnight Queens. These are pretty easy enemies, as they don't have too much health and are weak to wind, so they should go down within two rounds. You will receive a Security Keycard for winning the fight, which is just what you need to unlock some doors in this Palace, including one you passed by earlier. That barred door only has some breakables inside, so you don't need to go back if you don't want.
Return to where you fought the Midnight Queens and continue north, through the next door. In this hallway, the first door you come across will be accessible by the keycard you just got and around the corner is another door that is being guarded by some Shadows. Ignore them and head through the locked door to find a vent you can crawl through, leading to the control room. There will be another guard in here, which you have to fight. The Auspicious Pachyderm is weak to Psy, so it should go down within two All-Out Attacks or so.
You receive a Members' Card off of the previous fight and thanks to Futaba's skills, you will now be able to use it in the casino to take the elevator you couldn't before. Ryuji points out another vent you can crawl through, so do that to end up in an adjacent room that has another keycard door. You can explore a bit to the south to find nothing of particular value, as the one room is a surveillance room you can't enter. So, use the stairs to the east and follow the path until you come to another keycard door that leads you back to the rafters above the main room.
Make your way back to the ground floor and use the Members' Card to take the elevator to the Members' Area (there is a Safe Room south from the elevator on the main floor). After some scenes, it looks like you will need to gamble in order to get to the next area, the high limit floor. There is another Safe Room off to the west, in the middle portion of the map here, if you wish to use it. Approach the desk and talk to the Shadow Dealer here to not only get 1,000 coins and a map, but also learn about the two playing areas to the left (Dice Area) and right (Slots Area) of the counter. Unfortunately, you can't do anything in the Slots Area yet, so head to the east to enter the Dice Area.
Dice Game Area
The objective to the dice area is to guess whether the dice total will be between 3-10 or 11-18. If you get a triple match on the dice (three 1s, for example), then you get triple the payout and triple 6s will quintuple your bet. However, if you play a few times, you learn that what Akechi said earlier rings true, as the games are truly rigged so you can't win, so you will need to find another way to get the 50,000 coins. North of where you initially entered is a vent you can crawl through to reach the backroom area of the Dice Area.
This area here can be slightly confusing, but your objective will be to get to the north to some stairs. To the west of where the long hallway is on the eastern side are some machinery you can jump over, so do that and enter the room just north of that for a chest ( Black Robe ). Now, take the hallway on the western side to the north and climb the stairs you see on your map (be careful of a Shadow that might be on the stairs). The room on the way to the stairs leading down just has a few breakables.
The first area back downstairs has two Shadows close together, so try and wait until they separate to take them down. For now, go south, west and south again to spot a small room on the map, which happens to be a Safe Room. The stairs to either side of this area just loop around to the other set of stairs, although there are a few breakables up there. The door to the east of the safe room has a breakable in it, so continue south and you will come to a room that is locked from this side. If you head to the northern side of the room, though, you can find a vent that lets you get inside, where you'll find a chest that has a Parrying Dagger .
Slightly north and west from that room with the chest is a door that will bring you to the cheating control room. Attack the guard there to get into a fight with a Wandering Reviver. This enemy is weak to both bless and wind skills, so it should go down without much trouble at all. After the battle is over, Akechi will come up with an idea on how to rig the games in the party's favor. Exit the backroom area and go to the marked dice room, where you will want to bet on the "11-18" option four times in a row. You should now have around 2500 coins after winning the rigged game. That's all you can do here, so exit back to the Members' Floor Lobby for a cutscene, with you getting another 3000 coins.
Slots Game Area
As soon as you enter the Slots Game Area, a Shadow will stop you and force you into a fight. These two Life-draining Spirits are something you might have seen before, but they are different now. They are weak to Nuke skills, so they should go down with relative ease, probably one All-Out Attack. After finishing the battle, look on the southern wall just before it opens up to spot a red screen. This control panel will be important in a bit, so remember where it is. There will be some waitresses posing as Shadows walking up and down the aisles, so watch out for them as you head west.
The one door at the end is blocked by lasers, so you won't be able to go through there. Go up the stairs nearby and follow this path until it goes back down some other stairs. From here, go north to find the locked door, but you will be able to open it from this side with your keycard. Now, head south and through the door that's leading east, looking for some boxes you can hop over to your north on the map. There will be two things here in this little hole, a green control terminal (remember this) and a treasure chest ( Smokestained Armor ). You're pretty much done here for now, so look at your map to see the door to the far west, which will lead you further into the Slots Area.
Your party will point out the big slot machine in the back, which is the one you want. Take out the two patrolling Shadows, then scope out the place for any breakables, as well as the big slot machine itself. It looks like you can win the 50,000 coins here, but it's highly likely the machine itself is rigged to make your lose. Head up either set of stairs and climb the wall on the southern side for a chest ( Ghillie Vest ), then climb the wall on the northern side to find the main control terminal.
Futaba can do her job at disabling the rigging, but not from here, as she mentions she needs access to both the red and green control terminals. One's by the entrance, while the other is in the passageway and it can be a bit confusing finding them both. However, both have been pointed out in this section of the walkthrough (complete with pictures), so they shouldn't be too difficult to find. Once you disable both, go and save in the lobby, then return to the big slot machine.
As Morgana points out, there is a 20% chance the rig won't work, which is why you saved. Play the slots and if you happen to lose, reload the save and try again. Once you win, you will have the 50,000 coins to buy the Member's Card for the high limit floor. There's nothing left to do here, so head straight to the lobby when given the option (might be a good idea to save again). Go to the counter and purchase the High Limit Card, as well as the Soma and Bead Chain, since you should have enough leftover for those (they're fairly rare and powerful healing items). Upon going back to the elevator, a guard will be there and you'll have to fight it.
The Final Measurer is annoying, as it isn't weak against anything, but it does resist ice/curse and absorbs wind, so don't use those. You are free to use anything else and if you have access to Lucky/Miracle Punch, then a critical and All-Out Attack should pretty much almost kill it. You want to quickly kill it, as it has access to Garudyne, Rakukaja and Diarahan, the last of which can heal the mini-boss completely. After the fight is over, use the elevator to go to the high limit floor, where you find out you can't advance, so it's back to the Palace's entrance to return to the real world, but there's something else you can do here.
By now, you should have reached level 51, which means you can fuse the final Persona for the Strength Confidant, Seth. It needs to have a High Counter on it, which can be done in one of two ways. The easiest way is to fuse Seth (advanced fusion that requires four Personas) and then use the High Counter skill card you received during the last big outing in Mementos (it dropped from Shadow Kiritani, AKA The Killer Who Cleans Up Trash request).
The other way is actually fusing and using skill inheritance. Seth is an advanced fusion that requires Isis, Thoth, Anubis and Horus. Three of the four are from Futaba's Palace, so you might have them from there or from inside Mementos. The lowest level Persona that has High Counter is Dakini (Empress), who learns it at level 52. Scathach + Thoth will get you Dakini and your current Empress Confidant should be enough to get the skill (will have to grind otherwise).
From there, fuse Dakini with Pixie to get Anubis, making sure to inherit High Counter. The only Persona you probably don't have is Horus, which has two fusions you could probably do right now. Either fuse Kushinada with Hecatoncheires, or go with Bugs and Anubis (if latter, inherit High Counter). Once you have all four, fuse them together to get Seth with High Counter, which you can show to the twins and max out the Strength Confidant. Not only do you gain the ability to fuse Zaou-Gongen, the ultimate Persona of the Strength Arcana, but you can actually fuse Persona of a higher level than you. However, you will have to pay some money to do that. You are now done at the Palace, so return to the real world, making sure you grab a Hanged Man Persona for tonight.
November 13th (Night)
When you get home, get a massage from Kawakami, then go and hang out with Iwai (don't forget the Hanged Man Persona).
Confidant: Pick "Are you sure he's alive?" for your first answer, then whatever you want for the next four responses, and either "Kaoru is really strong-willed" or "He's a cool kid, huh?" for the last one.