Well I got through Cave of Remembrance today and reached this place. The Garden of Assemblage.
It's a secret area next to Hollow Bastions restoration site. Each one of those doors leads to one of the Org XIII bosses, but very powered up versions of them. They all have more HP than Sephiroth and are harder to beat.
I wanted to fight Axel first, since I thought he would be the easiest one, but I accidentally chose Xemnas. (Their weapon icon looks a bit similar.) Xemnas is a lot harder than before. He does a Omnislash like attack quite often and the screen goes dark. It looks like the moves he used in KH 1: FM. When you finally beat him (it took about 10 minutes or longer.) you get to fight against his final form. He starts to spam some electrick sphere attacks I've never seen before. And then he did something on me that started a reaction command. I lost my keyblade but Riku picked it up and threwe it to Sora right before Xemnas hit him. Then I was supposed to press Triangle, but I didn't react fast enough and died. o.o'

So I tried Axel, thinking it would be easier. But apparently when fighting him now, due to the heat your HP goes down constantly, and fast. I didn't last very long.
Same for when I fought some of the others. It's really hard.

Well I'll try to beat some of them later, but I think I need to Level up a lot.

Is there any added bonus to all the work you're doing? Or is this just for people who wanted harder Organization members?? I don't really understand the purpose lol

I think the only actual reward you get is that you can equip a silver crown on your head. There might be more though, I'm not sure. But the Order members are not just stronger, most/all of them have new attacks and some have new Triangle cutscene events that look cool. And also, you can come here and fight them at any time. Even after you beat them you can still challenge any one you want over and over. So basically you have access to your favorite boss battles any time you want. And it's right next to Hollow Bastions save point outside. (After you beat the Cave of Remembrance a new shortcut path will be revealed so that you can get back to that place in about 5 seconds.)

And an update. I beat six of them so far.

Axel was really hard until I realised how to get rid of the fire that constantly drains my HP.
Vexen was the easiest one so far. Pretty straight forward, except for when he does his new ice shield move.
Saix was the most annoying one so far. It was near impossible to get a hold of one of his weapons, because they vanish much quicker than before. And I think I fought him for about 30 minutes before I finally beat him. *_*
Larxene was also pretty straight forward like the one with the shield, but she was really powerful.
Xigbar was really fast, powerful and spammy, and nearly killed me many times, but somehow I beat him on the first try.
Roxas was pretty tough. A lot harder than before. The hardest battle of the six so far, and I had to try several times before I was able to win. When his HP is down to about 4 bars he's almost impossible to hut because he doesn't seem to flinch when you hit him any more, and he keeps spamming really powerful attacks.

I tried Marluxia but it was too hard. Same for Xemnas. He now fights with some moves from the first Final Mix. And his second (last) form has some new attacks as well.

Haha I'm glad you're enjoying that then, cause I don't really think about those things that much when I play. I like exploring a plotline and storyline more than the actual gameplay. I'm not a big fan of fighting boss battles, but more concerned with the cutscenes afterward.