Lol. I beat the Palace, and put the game down.
Soo... here's the deal.
It's required to get the Doctor to lv 2. This will get you access to Heal All medication (Party wide 100HP). You'll need 5 or 6 of these to counter Kamoshida's kill spike while waiting on Ryuji's slow ass to steal the crown. You NEED two people to attack each round just to progress Ryuji, so he doesn't get caught.
The basic idea: Use Agi and Garu to hit Kamoshida, and Joker uses a Heal All item if needed, or use a single heal item. If MP is a problem, have Joker user Def Down with Genbu, and smack him with melee to do equivalent damage.
Climbing the tower is quite aggravating, as I needed Silky for ice elemetns to take care of Berith (the knight on the horse), as he can 1 shot a character every turn.
It got super aggrivating to deal with that. (Note: if you are not level 6 by time the tutorial tells you about viewing people's difficulty view thief mode, you are too low and need to turn around)
A quick fix for an early game is Incubus' sleep power, which will give your team a free round to take a swing at things.
Try not to heal inside the fight. Reserve your time for keeping enemies down due to weakness shots from elements and guns.
Don't be afraid to save, first, run into a fight, and experiment to learn who's weak to what, then reload.
I had to grind quite a bit, and I kept starting from the entrance, so I can keep stealing everything that's not nailed down, just to accommodate the very expensive heal all medication.
As for the doctor:
You may need to restart your game for this, but go to the library, get the boot that increases guts, study in the library for a chance to level guts, and use the bookshelf at night to read the book. Get your guts to lv 2 ASAP so you can get the doctor's second trial.
I honestly don't know how the Kamoshida fight is possible without it.
Unless you use the DLC persona =P