After the opera, Locke, Celes, and the others successfully board Setzer's airship and convince him to take them to Vector.
Go to Vector
Make sure to equip weapons and armor on Celes. Talk to Setzer to get him to go to Vector. After you land, you can go back into the airship to heal up for free (talk to the guy on the left). You can also buy items from a merchant inside of the airship (the guy on the right).
Grass and Forests:
76. ChickenLip/Chiknlip/Litwor Chicken
Besides Vector, there are other towns on the continent that you can visit if you wish. Albrook is nearby. Tzen is to the northwest, and Maranda is to the southwest. Vector is in the center of the continent.
If you bring Sabin with you, try leveling him up to level 15, because then he will learn the Blitz Fire Dance/Rising Phoenix, which is very helpful in the next area.
In fact, try to make everyone at least level 16 before you go, because there are enemies in the factory that can use L.4 Flare/Lv.4 Flare (which will kill everyone who is at level 16 since it's divisible by 4) and L.5 Doom/Lv.5 Death (which will kill everyone who is at level 15 since it's divisible by 5). If everyone is already level 16 or so when you enter the Factory, then your levels will have reached 17 by the time you reach the part of the factory where there are enemies that do those level-based attacks. This enemy also knows L.3 Muddle/Lv.3 Confuse, which will affect you at level 18, but you can avoid this with Relics.
In Vector, go to the left and enter the skinny house. Tell the woman that you won't pledge to the Empire. Defeat the guards that appear. After this, the woman will heal you up for free any time you talk to her.
Go to the east side of Vector to find someone hiding behind a box. Talk to him, and while he is creating a diversion, jump onto the box and make your way along the tracks. Go north at the sidestreet and you will enter the Magitek Factory.
80. Pipsqueak/Onion Knight
You will not have any other opportunity to fight the monsters that appear in the Magitek Factory.
Use magic against these enemies whenever possible, because the enemies here are all strong against physical attacks. Edgar's Bio Blaster tool does elemental damage, so try using it if you have it. Many of these enemies are weak to Lightning and Water.
If you fight ProtoArmors, don't hit them with regular Fight/Attack, or they will counterattack. Celes can use Runic to absorb their Tek Laser/Magitek Laser attacks. Lightning spells work best against them. If a Proto Armor is by itself, it may use the highly damaging Launcher attack.
After going down the two flights of stairs, you will see pipes to your left. Go straight through the topmost pipe to reach a chest. Then go north to where the hook is going back and forth. When it comes close, press A to grab onto it. You will automatically get off on the other side.
Go right, and down the rightmost pipe to reach the treasure chest. Then climb up through the rightmost pipe and climb down through the leftmost pipe to go onto a conveyor belt.
After getting off of the conveyor belt, open the chest to the left, then walk onto the conveyor belt to the right. Open the nearby chest, then go south and open the chest below the crate, then walk onto the nearby conveyor belt.
Go to the bottom-left corner of this room to find a chest. Then go up the nearby stairs and go north, then go through the north door to find another chest. Then go south again and go down the stairs.
Go east from the stairs until you hit a wall, then go south until you hit a wall, then go west and south through a hard-to-see door. There is a chest to the left. Exit this area through the door that you came through. Then go east, and look for a small room to the south. Go through the door and go all the way to the left, then press A to open a hidden chest. Leave the small room and go east, up the stairs. Open the nearby chest, then go down the stairs again, then go west and then north to go back to the large area that you were in earlier.
Go to the northeast corner of the area and use the stairs there. Go east until you see some crates to the right. Go slightly south and walk between the crates to enter the pipe in the wall. Go south and then go east when you can, into a side room. Open the two chests there. Go west to enter the pipe again, and go south until you fall. Afterward, walk onto the conveyor belt that has MagiTek Armors being put onto it (walk onto it from the side, not from above).
Go south and you see Kefka. Go down onto the conveyor belt where he throws the Espers.
Before talking to the Espers, go through the far left door to find a save point. Use a Tent there to heal up if you wish. Then talk to the Esper on the left to begin the battle.
Ifrit and Shiva
Ifrit is vulnerable to Ice, and Shiva is vulnerable to Fire. Ifrit absorbs Fire and nullifies all other types of magic besides Ice. Likewise, Shiva absorbs Ice and nullifies all other types of magic besides Fire. Using Runic is not recommended because you will want to attack with magic if possible. Note that neither Esper has anything to steal. If you attack Ifrit three times in a row with magic, he will counterattack with Fire 3/Firaga. Similarly, if Shiva is hit three times in a row with magic, she will counterattack with Ice 3/Blizzaga. There is a chance that Ifrit will counterattack with Fire after any attack, and there is a chance that Shiva will counterattack with Ice after any attack. After Ifrit is hit five times with any damaging attack, he disappears and Shiva appears, and after Shiva is hit five times with any damaging attack, she disappears and Ifrit appears. Technically, it is possible to run away from the battle while Ifrit and Shiva are switching places, but it is difficult to do so before the other Esper appears on screen.
Once Ifrit says that he senses a kindred spirit, the Espers will not attack. After the battle, talk to both of the Espers, then take the magicite. Save, then go into the room that Shiva was blocking.
Go north through the straightforward path. You eventually reach the first tube room.
First Tube Room
Go west through the tube room. When you are below the leftmost tube, go south and west into the wall until you can't go any farther south and west, then face north and press A to open a hidden chest. Then go back up to the main part of the tube room, and go through the door in the northwest corner.
Go north in the next room and talk to the creature that is blocking the door. You will start a boss battle with Number 024.
Number 024 can use a move called WallChange/Barrier Change, which makes it vulnerable to a specific type of magic, and makes it absorb other types of magic. Number 024 will use magic attacks that are the opposite of its weakness (so if it uses Fire, it's weak to Ice). You can use Sleep and Imp on Number 024 to limit its ability to attack. Imp will prevent Number 024 from using magic anymore, but it will always do a critical hit whenever it attacks, requiring you to heal often. Usually Number 024 has a Rune Edge/Rune Blade to steal, but there is a slight chance that it will be a Drainer/Blood Sword instead.
After the battle, go into the next room and unequip Celes of everything. Then go north as far as you can, and flip the switch to get more Magicite.
When you're back in control, follow Cid onto the platform, then save at the save point (your HP and MP should already be maxed out right now). Equip Locke with Flame Sabre/Flametongue if you have it.
If you have Sabin with you, move him to the top of your party if you want to encounter the red Mag Roader/MagRoadr/Magna Roader, a rare enemy. If having Sabin at the top of the party doesn't work, you will have to reload from the last save point and try putting someone else in the top slot.
You may wish to equip the Phantom Esper on somebody, because using it in the next boss battle renders you immune to all of that boss's attacks.
When you are ready to continue, talk to Cid. He will push you onto a mine cart, and you will have to have four enemy encounters, and a boss battle, on your way out of the Magitek Factory. You might want to use the Phantom Esper in battle (choose Magic, then press up and choose the Esper) during the fourth normal enemy encounter.
87. Red Mag Roader/MagRoadr/Magna Roader
Don't attack the arms. Just attack Number 128's body. If you do kill both of Number 128's arms, there is a chance that Number 128 will use the Blaster attack, which is likely to kill everybody and give you a game over. Number 128 counterattacks all attacks with Red Feast/Blood Feast. It absorbs Ice-elemental attacks and has no elemental weaknesses. There is a small chance that it is carrying a rare weapon that you can steal (Tempest/Kazekiri for Cyan).
When you're back in Vector, technically you can go back into the Magitek Factory, but you can't go very far into it anymore. Use the save point, then go southward along the tracks until Setzer comes to get you.
After Setzer arrives, watch the cut scene. Soon, a battle will begin.
Left Crane and Right Crane
You should use physical attacks against the cranes. If you use Setzer's Slot attacks, try matching three diamonds, or three airships, or three birds. But be warned: if you get a 7, there is a high probability that you will get two 7s and a BAR, which will kill all of your party members, giving you an instant game over. The Left Crane absorbs Lightning and will counterattack with GigaVolt if hit with three lightning attacks. The Right Crane absorbs Fire and will counterattack with Fire 3/Firaga if hit with three fire attacks. The cranes can heal each other. Both cranes are weak to Water, so the Bismark/Bismarck Esper attack can be used. After one crane dies, the other uses TekBarrier/Magitek Barrier, which gives it Safe/Protect and Rflect/Reflect.
After the battle, you will return to Zozo to check on Terra. After the cut scene, there will be a scene in the Esper World.
In the Esper World, there are no treasures to collect. As Maduin, exit the room, then go north toward the large cave opening, and check on the girl. Choose "return together", then talk to the girl in the bed. Then get out of your own bed and go up to the large cave opening again. Talk to the youth who is blocking the way, then go into the cave. Go north and talk to the girl.
After a cut scene where Gestahl enters the Esper World with troops, go south and talk to the Elder. Then talk to the Esper by the door, then go outside. Go west from the Elder's house until you see a wooden bridge, then go north from that bridge, and into the large cave again. When Gestahl and the others disappear, go north and talk to Madonna/Madeline.
After this, you will all board the airship and Setzer will tell you how the controls work. While flying, press X to go inside the airship, where you can change your party members, heal up, and buy things from the merchant. You can press START to toggle the map.
Your next destination is the Cave to the Sealed Gate, which is in the east part of the Empire's Continent, but before that, you should use the Airship to explore the world.