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The first forced trip to Futaba’s palace involves going in, talking to her, and leaving without fights
When you actually do the palace, you need to go to the outskirts surrounding the pyramid, and you need to trap an enemy, see our video walkthrough below.
The palace is mildly annoying because it does have a lot of platforming with hidden sections all around, use L2 to look out for places where you can jump/fall or grapple, and be sure to pick up crystals to give to statues later
You will keep unlocking shortcuts as you go down the doors of the main palace.
Be careful of the anubis enemies, they may use instant death attacks on your main character. Use the safe rooms to save often if you can.

There are puzzles where you need to move a scrambled puzzle into the correct picture, it’s not too bad. For the later scrambled puzzle, you need to rotate the pieces as well.
As you reach the second-half of the dungeon, you will see a puzzle that will vary slightly between players.
A code is randomly generated in the long hall room that has blue, red, and white sphere holograms are. Let’s say your code is B01010, the 0’s mean no spheres and the 1’s mean yes spheres, so you’d see the blue sphere there, then the right one needs to be off, then the next right one is on, then the next right one is off, etc.
There’s a second puzzle in that room too, involving numbers and R, R refers to the red sphere now, it’s the same logic, look for the right sphere, and move to the left each time, 0 is off, 1 is on.
Your code will be different because it is randomly generated between players.

The boss is tricky for once. Make sure you have powerful physical attacks on some characters!
You can still target the boss with guns or magic attacks because they’re long-ranged, but these attacks are kinda weak. Why did I say to make sure you have physical attacks available? You need them for later.
Don’t bother trying to damage the boss too much with long-ranged attacks.
You really just need to keep defending until Futaba joins.
Once Futaba joins, she will tell you to use the ballista. Have one of your characters use the ballista, and start buffing your team in the mean-time.
Afterwards, the ballista will knock the boss onto the platform, now’s the time to use physical attacks. It’s not an official weakness, but your physical attacks will do an extremely high amount of damage. When she’s in pain on the platform, make sure to use physical attacks!
We didn’t know until we ran out of SP that physical attacks did such a multiplied damage against the boss! A simple dormin rush did 1360 damage to her!
Rinse and repeat the process. If the boss still has health, eventually you will be able to use the ballista again, when she falls use physical attacks.

Futaba Palace Walkthrough with Will Seeds – Persona 5 Royal