Geno Dome Sidequest - 2300 AD Middle Ages
When you speak to the Old Man in The End of Time at the end of the game, the third item on his list of sidequests for you is, "There's a task to be done in the future, where machinery originated." This is making reference to the Geno Dome which is found in the eastern portion of 2300 AD.
For this dungeon you will need to put Robo in charge of your group since he'll be required to complete some of the puzzles and is involved in this dungeon's storyline. The main puzzle of this dungeon involves you having to collect two Poyozo Dolls, they're the white fluffy creatures shown in the two screen shots below.
Once acquired, these creatures can be placed on the green circles next to the large door on the second floor, which leads to this dungeon's boss.
First Poyozo: In order to reach the first doll (screen shot on the left) you'll need to reverse the escalator that's on the first floor of the dungeon. The room to do this is at the top of the escalator. After you reverse it, grab a charge with robo at the central charge point and run allll the way around the dungeon to unlock the door furthest from the computer terminal. The reversed escalator will give you the speed boost you need to make it.
There'll be a droid in this room who you will want to escort around the entire dungeon to the far southwestern corner where you see my standing in the screen shot above. If you 'introduce' these two droids you'll be able to get by them and grab the doll.
Second Poyozo: The second doll is much easier to obtain. In the screen shot on the right, where you see the three switches, pull the one in the middle. This will allow you entry into the charge area for Robo to unlock the door. The doll is just inside the door and easy to grab.
After collecting both Poyozo Dolls and heading up to the second floor, you'll engage in a one on one fight with Atropos, a pink robot who knows Robo aka Prometheus. Defeating Atropos will give Robo a permanent upgrade of 3 Speed and 10 Magic Defense.
Place the two Poyozo Dolls onto the green circles to open the large door, go into that room to speak with the Mother Brain, who is also the boss of this dungeon. The battle with her is a pretty easy one, take out the three computers when the battle starts with any level 2 magic attack then use your strongest Techs on Mother Brain until she goes down. The reward will be Robo's Ultimate Weapons.