Take Robo to the future to complete the Origin of Machines sidequest.
Put Robo in the lead of your party, and equip everyone with Shadow-absorbing armor.
Go to 2300 A.D. and fly to Geno Dome, which is on an island by itself in the southeast of the world map (press Select to see it). If you are having trouble finding it, go to the Northern Ruins in 600 A.D. or 1000 A.D. and travel to 2300 A.D. from there, and you should be near the island.
Go inside and check on the monitor on the wall to the left. Go through the door, and if you want to leave the dome after this, go back and the door will be open again. Equip Shadow-absorbing armor if you have not already.
The conveyor belt leads to 5 fights, and with the Shadow-absorbing armor equipped, you can just use physical attacks, healing the unprotected party member as needed.
When you are done, go through the door to the north. If you want to use the conveyor belt to earn more experience, go to the southeast corner of the room. You can check on the sparkle there to enter a Dust Chute that brings you back to the beginning of Geno Dome, letting you go through the conveyor belt over again, which yields a lot of experience. After you beat Geno Dome's boss, you won't be able to use the conveyor belt again.
For reference, the total EXP you gain from the conveyor belt is 8286, the total skill points are 144, and the total G are 10,200.
After the conveyor belt room, go west, then north up the first passage. One of the robots will become electrified. Follow it. When it makes the door open, hurry through before the robot goes in. Open the chests to get a Full Tonic and 50000 G. Leave the room.
Go back to where you saw the robot charge itself, and approach the chest in the corner and defeat the enemies that attack. Open the chest to get a Full Tonic. You can check on the computer for some information. One of the things that it will tell you is that you need to collect two dolls to reach the boss.
To get the first doll, go to the west side of the room and go through the door there, then go north. Defeat the Laser Guards, then go north to the three switches on the wall. Check on the left switch and the right switch, so that the middle is still green.
This unlocks the energy-activated pod. Go south through the door, then go east toward the computer on the wall. Enter the charging pod to the left of the computer, then go west and north through the door, and enter the energy-activated pod to the left of where you defeated the Laser Guards. Go through the door that opens and take the doll. Wait a moment and then check behind where it was to get a Speed Tab.
Go to the southeast of the area and go through the door near the sparkle. Take the elevator up.
Save at the save point if you wish, then go through the door north of you. Before you run up the hall, take the Power Tab at the bottom right. Then go north and defeat the enemies. Go north through the door and take the elevator down.
To your left, there is a secret passage. There is a hidden Magic Tab in it. Go west into the secret passage, then keep trying to go north and west. If you do it correctly, you will stop being able to go north and west. Press A to check that area, and you will find the Magic Tab.
From the place where the hidden Magic Tab was, go southeast until you can go west through the hidden passage, then go south, then east to the switch on the wall. Flip the switch, then go back through the hidden passage until you are near the door where you entered this area.
Go south, defeat the Laser Guards, and flip the nearby wall switch to deactivate the laser barrier. Go as far west as you can go, then check on the wall switch to open the wall pod. Now go east to the conveyor belt, and run all the way south on it, then go east and make your way along the path until you can go north through the first corridor. Then go northeast and enter the charging pod to the left of the computer on the wall. Then quickly go back the way you came: southwest, then south through the narrow corridor, then east to the corner, then north, west to the conveyor belt, north up the conveyor belt, and west to the pod in the wall. Quickly enter the wall pod to unlock the door. If you didn't make it in time, you will need to go back and try again.
Once you unlock the door, go north through it. Open the chests to get a HyperEther and a Full Ether. Then check on the robot and it will go south out of the room. When you leave this room, the robot will follow you. It is slow and can get stuck near walls, so go slowly and make sure that it catches up to you. Take the robot east to the conveyor belt (you may need to go north on the conveyor belt to get the robot unstuck from the wall), then go south on the conveyor belt with the robot, then east, then south, then all the way to the west, and finally, go north to the other robot. Move around near the northern robot until the southern robot gets stuck facing the northern robot. Afterward, you can open the chest on the left to get a Vigil Hat. Then check on the doll to take it.
Now go south, then east to the southeast corner of the area, and go through the door there. Use the elevator. Don't save or use a Shelter yet. Go south and defeat the Laser Guards, then open the chest to get a Lapis. Then go north to the save point, save and use a Shelter, or if you don't have one, at least make sure Robo has full health. Then equip Robo with the Red Mail if you have it. If Lucca is in your party, the next part will have additional dialogue. Go south from the save point, then go west from the treasure chest. Watch the cutscene.
You don't have to attack Atropos at all to win this battle, but you should use Cure Beam on yourself as needed. She will go through a specific set of moves: RocketPunch, Cure Beam, Laser Spin, Atropos Tackle, Cure Beam, Uzzi Punch, and then she will do Area Bomb six times. After the sixth time, she will say "I--" and will explode, damaging you a small amount. Then the battle will end. Watch the cutscene that follows.
Geno Dome, Part 2
The ribbon is not an accessory, but rather a permanent addition that boosts Robo's stats. Afterward, go north and walk toward the switch to the right of the lasers. Robo will jump up and open the way. (If he does not, go south from the switch, then north toward it again.) Go into the room and open the chest to get a MegaElixir. There is a Magic Tab in the bottom right corner of the room.
Exit this room, then go west and follow the path. Go south down the ladder, and follow the path to find a chest that contains 15000 G. Go north through the door and watch the cutscene. Go east and south to reach a chest that contains a Full Ether. Then go back the way you came. Equip Robo with Shadow-absorbing armor. After you go up the ladder, go northwest and defeat the Laser Guards. Then go north and defeat more Laser Guards.
Check on the green spots to the left and right to place the dolls there. Watch the gate open, then you may wish to go back to the save point to save and use a Shelter before you return to this gate, because there will be a battle.
You may wish to have Ayla in your party, equipped with a Charm Top, because you can Charm a Blue Mail from the next enemy. It is recommended to equip one character with the Amulet, another with a Vigil Hat, and another with a Sight Cap, to protect everyone from the Chaos status. It is helpful to equip all of your party members with Black Mails and the Black Vest if possible.
You can Charm a Blue Mail from MotherBrain's head. The Displays heal MotherBrain frequently, but don't kill all of them; just kill two. If you kill all of them, MotherBrain gets progressively stronger and more difficult to beat, and uses an increasingly damaging attack every round. If you did not equip everyone with status-protecting gear, if anyone gets inflicted with the Chaos status, use a Heal on that person immediately to prevent them from accidentally killing the last Display. Use your best physical Dual and Single Techs. If Robo and Ayla are in your party, you can cast Boogie on the last remaining Display to stop it from healing MotherBrain.
Geno Dome, Part 3
Now you have Robo's Terra Arm and Crisis Arm, and the Dome is shut down and you can't get in anymore.
A note about the Crisis Arm: the damage that it does depends on Robo's current HP. Specifically, it depends on the ones digit of his current HP. The higher this number is, the better. If his HP ends in a 2, he will do roughly normal damage. If it ends in a 1, he will do less damage, and if it ends in a 0, he will miss. Anything higher than 2 will do higher than normal damage.