It appears this flying fortress is where Krom is holed up, so your objective is laid out for you. Once you finally regain control, you will see some stairs off to your right, as well as a path leading south. The southern way will allow you to head back to the imperial capital, specifically the Command Base. Anyways, when you're ready to continue, walk up the stairs and keep going east to view a scene at the top of the next set of stairs. There will be some enemies here and you're free to take them out, but be aware that Blitzpods can counter when you attack them. Unfortunately, this way is a dead end, although you can see a lever on the ledge above.
Double back to the split and head north this time, where you'll notice a door above you, a sparkle on the ground and another path leading you to the west. Continue in that direction, vanquishing the group of enemies before you, then keep going until you come to another dead end. Luckily, though, there is a pillar on the ground that you can destroy with your vulcosuits, so go ahead and do that, as well as break the next one to come to a lever. Pulling this will unlock the gate to the left of it, but it appears you're still at a lost on where to go. To the right of the lever just pulled, you should spot a ladder on the wall that might be a little hard to see.
Climb the ladder, fight off the enemies up here, making note to be careful with the Patrolbots, as they can instantly kill a character with Murder Needle. There is a path to the northwest that leads to a discolored block, which is an elevator. Take this down and fight the group of enemies here and open the chest here for 3 M Potions. Return to the previous area and follow the path as it goes south, leading to a drop off and another lever, this one unlocking the gate next to it. Go through this passage to find another stone vulcosuit blockade, which has a blue sparkle behind it. Grab it, then return to the split you just happened upon, dropping off to the south and fighting the group of enemies nearby. Ascend the stairs to find another group of enemies waiting for you.
Just north of you is a chest, but it is behind a gate. For now, just drop down to your south and continue south to a switch, unlocking a shortcut, then break the rocks on the right, which reveals a path that goes around to some enemies and behind the chest you just saw, allowing you to open it for 3 Silver Coins. It may look like a dead end here, but the square-shaped dead end is actually an elevator, shooting you up to a new area. Destroy the debris in your way and travel west to find a doorway, but continue west (more debris) to find a sparkle at the end here, which yields the Apocalypse artifact knowledge. Enter the doorway to delve deeper into the flying fortress.
In this new area, travel north and when you see the first set of stairs to your left, take them. This will lead to a room with some enemies, probably Guardbots, an upgraded version of the Patrolbots from earlier. More enemies will be in the room north of the first group, so get rid of them and carry on. You will come across two switches off to the right, with the first one opening a door you can't reach, but the second opens a door right next to it. Head through this, grab the sparkle on the ground, then continue north, through the first door you likely opened.
You'll encounter more enemies here, probably a new one called a Crasher, which is the same as the Slasher you fought in the Catacombs not too long ago. There is a sparkle in the northeast corner of this room, as well as two different ways to go, left and right. For now, go left, all the way to the end, to find a chest with 3 Spring Waters in it. You passed another path on the way to the chest, so double back and travel along that one, opting for the left path here to fight more enemies. They will be guarding a sparkle that yields some new artifact knowledge, Avenger.
In the previous room, continue to the east until you come to another with a save point. On the northern wall of this room is another switch you can hit, which opens the door just to the left of it. Heal up at the save point, should you need it, then run south to hit another switch, opening another door close to your location (plus, you saw someone standing in that room). If you have any beneficial dishes on you, consume one now, then go confront that person to trigger a boss fight.
BOSS - Zemrode (3)
If you remembered anything from the previous two encounters with Zemrode, then it's that he is very fast and will likely get multiple attacks on you during your own turns. Because of that, you want to finish him quickly, but you also want to be careful and avoid unnecessary deaths for your party members. Despite Zemrode's seemingly low health, he gets two lives during this battle, thanks to Revitalize. Whenever you deplete his health the first time, he will use previously mentioned skill to instantly KO a party member and refill his health back to full.
As for his attacks, Zemrode has quite a few and they can pretty much all hurt. He has access to five different elemental sword techniques, all of which hit four times, meaning some hits can miss and some can critically hit (the latter seems more likely to happen). You have thunder, ice, wind, fire and earth, and some of them even have ailments attached to them. Lightning Bolt Thrust can inflict oblivion, which blocks you from using items, Raging Flame Thrust has scald, which acts like a poison, and Violent Gale Thrust can give a character slow.
Those aren't Zemrode's dangerous attacks, though, as Peerless Might only hits once, but if it crits, then you might be looking at 200+ damage (200 HP is your threshold during this battle). Overgrown is a multi-hit skill that can deal upwards of 200 damage, as well, but it is spread across 7 hits. The worst attack is called All Things and seems to happen as he gets lower on health. This can hit everyone for around 140+ damage, which is a big nuisance to try and heal. Note that Zemrode doesn't have any new attacks that occur after he uses Revitalize. It does appear that Zemrode's physical evasion is pretty high, but don't let that deter you from using those kinds of skills.
Healing is definitely a big issue during this battle, especially with the CT count working against you and the potential oblivion ailment from Lightning Bolt Thrust making your items unusable. Sherra is one of the best party members, though, since X-Heal can mend the wounds of everyone, plus Heal is a good back up and Refresh will get rid of any ailments. Kanata is another good user, despite the range of Aura, but Calamity helps in mitigating some of the damage that Zemrode can toss out. The other two characters are up to you, but damage dealers are something you will want, especially Obaro for his magical prowess.
Note: The Old Key you receive from winning against Zemrode will allow you to finally open that locked chest in the wardroom.
It might take a few tries to fell Zemrode, but he will eventually go down. With him finally out of the way, feel free to return to the save point if you want to heal your party. Return to Zemrode's room and follow the western path here and as it turns south, you should see a diversion to your east. This first route will take you to a dead end with a chest, which contains a Phantom Fang weapon for Lumina. South of that is another path, which will eventually lead to a pack of enemies, so get rid of those and take the elevator just north of them. There's not much here, except for a save point, which can only mean one thing...well, not quite yet.
Use the save point to heal up and save, then descend the stairs to your left. After a minor distraction, a scene will play out and you'll encounter the next boss.
BOSS - Neo Rattler
Neo Rattler is not much different than the Death Rattler you fought previously, except it's stronger of course. In fact, it has a lot of the same skills as it did, like Light Surge. Luckily, this move only hits straight in front of its cannons, so positioning yourself off to the sides will make that attack nothing. Outside of that, it has a variety of gas moves, like Sleeping Gas and Toxic Gas. The most annoying of these is Nerve Gas, which can inflict paralysis, oblivion and/or silence. Having a health supply of Panaceas on hand, or Sherra with Refresh, will help in negating these.
Now, the boss will likely open up with Giga Proton Beam, which not only does 160+ damage to the entire party, but it also has a chance to instantly kill your characters, too. That means you'll need to resurrect fallen members should they get hit with the latter. Fusillade and Bullet Barrage are its projectile attacks, which can deal upwards of 150+ damage to multiple characters. Note that Fusillade will only hit characters close to one another, while Bullet Barrage will hit everyone. It also has Flamethrower, which can probably deal just as much damage as the previous attacks.
If you remember the previous encounter, then you might recall Barrier. Neo Rattler has similar abilities here, as Shield Barrier will raise its physical evasion (basically evades all physical skills) and Magic Barrier will make your magical attacks be reflected. To add insult to injury, Neo Rattler still has Meltdown when it perishes, so you want to make sure you're at full health when you kill the thing. Note that you can negate a lot of Meltdown's damage by inflicting it with Physical Mar right before you defeat it, putting the damage to around 100 or so. The same strategy you used in the previous battle will work here, too. Just stick characters to the side to avoid Light Surge and then do the same tactic of lowering its physical attack while using something like Guardian to null its biggest damage dealers.
With Neo Rattler out of the way, feel free to explore this little area to find nothing at all, so go north for some scenes. It may look like another boss is in order, but that is a lie, as things play out on their own and you'll eventually return to the imperial capital...