Kefka's Tower is designed to some degree to punish intuition. If you start with party 1, you're going to get stuck waiting for party 3, and then again waiting for party 2. Party 2 is free to clear their section, but must fight Atma before they can access a save point. Party 3 has it nice and easy, with an accessible save point right before a boss fight. For that reason, I recommend you start with party 3. That said, you can freely switch between all three groups as much as you want, aside from having to hit switches for party 1.
Outside Encounters
The largest single part of Kefka's Tower is the Outside area where all three parties start. You'll be entering and exiting this area a lot, and the encounters here never change.
The oddest encounter is one with four Vectaurs. It's odd only because they enter the screen in a blur, and all stand on top of each other. It's not even immediately clear that there are four of them. But there are, and they can be targeted like any other Monsters in battle, though it's hard to keep track of which one you're on. It's best to stick to multi-target attacks or just hit the one in front. Vectaurs themselves are a lot less interesting than their Encounter mechanics. They'll normally attack for moderate damage, and every other round they can use a fairly weak Fire Ball or their ×1.5 damage Tusk special. They don't counter attacks, and they are weak to both Ice and Water. With only 2,800 HP, they are one of the weaker Monsters to be found in Kefka's Tower.
The next combination is a Brontaur and an Evil Oscar. Brontaurs' basic attacks aren't so bad, but they can use Wail for quintuple damage as early as the first round. They'll follow that up with Lifeshaver, possibly twice consecutively, before another normal attack or Wail. Their last two rounds before starting over their sequence and be Atomic Ray, Lifeshaver, or Wail, all of which are quite powerful. With over 10,000 HP, it can be tough to take them down before they use any of their nastier attacks. You might want to wait until their early Lifeshaver blitz is over to hit their Ice weakness hard.
Evil Oscars look like Mad Oscars but are considerably tougher. They have 7,000 HP and absorb every Element except their weak point, which is Fire. They won't actively do anything but attack normally unless they're the last Monster left, at which point they'll start using Sour Mouth to inflict a variety of status ailments. They can counter Magic with their Wound special, Demon Kiss. Fire 3 from a powerful spellcaster may be enough to take them out in one shot and avoid the counterattack, but otherwise you may want to focus on physical attacks and special Abilities.
The final Encounter Outside combines a Vectaur, a Evil Oscar, and a GtBehemoth. These giant creatures may counter with a devastating Hay Maker and can use Meteor for upwards of 1,000 damage on every even turn of combat. They have 11,000 HP and no Elemental vulnerabilities. Meteor is your biggest concern during this fight, so the GtBehemoth should be your top priority.
Party 3's Path
Head south from the starting point, taking note of the direction the conveyors are moving. There is a Red Cap in the chest near the door here. This door leads to Treasures on the MagiTek Factory North walkway via the right side of the Double Path. This path contains Encounters against pairs of Brontaurs or trios of Evil Oscars.
You'll find a Nutkin Suit and a Gauntlet on the MagiTek Factory North walkway, along with some Encounters specific to this walkway. All of the Monsters here are mechanical, with vulnerabilities to Thunder and Water. The Prometheus can use the powerful Shrapnel attack. It can counter Fight with the nasty Fire attack S. Cross, or Magic with the Character-Freezing N. Cross. Try to hit their weaknesses in some other way to avoid these.
Scullions have 27,000 HP and good resistance to both physical and magic damage. They'll open by inflicting a Character with Condemned using their Gamma Rays, which gives you time to attack before they begin their real onslaught. Grav Bomb, Launcher, WaveCannon, and Atomic Ray are all in the Scullion's arsenal. They'll use Atomic Ray one last time when they finally perish.
You may also run into a trio of Innocs here. They open by inflicting Muddled with BrainBlast, then proceed to use Cold Dust and Plasma. Every fifth round, they may mix in L? Pearl. They have 6,600 HP each, and a powerful shot of Bolt 3 is potentially your best offensive option.
Once you have the Treasures, backtrack to the Outside area and head for the southern doorway. This leads to the Tunnel Entrance and more encounters with Brontaurs and Evil Oscars. Continue on to MagiTek Factory South. You'll see a nearby chest containing a Hero Ring. A hidden path through the southern wall leads to a small room with an Aegis Shld. You'll have to blindly maneuver a bit to access it.
The MagiTek Factory South and the lower areas of the MagiTek Factory North feature the same Encounters against machines weak to Thunder and Water. You'll often be attacked by a pair of Fortises. They will attack with Snowball, Fire Ball, or Missile. Of the three, only Fire Ball does normal damage; the other two deal fractional damage. If you hit them with Thunder, they will counter with a combination of Double Arm and a basic attack, though neither is particularly powerful.
The less common Encounter in the area is against two Duellers supported by a Sky Base. Both feature nasty counterattacks. Duellers have a powerful Megashock special, but often use L.5 Doom and L.4 Flare. They can counter non-fatal attacks with Shrapnel, so try to take them out in as few hits as possible. The Sky Base will open with L.5 Doom, then start using Mind Slap to inflict Stop. They may also cast Doom given enough time. They will counter anything but Fight with anywhere from zero to four uses of the Wound-inducing Blaster. Fight them to death if possible. They won't counter the finishing blow, so a substantially powerful Thunder attack also works.
When you're ready, head north. You'll see two conveyor belts. Hop on the one headed away from the area to pass through the MagiTek Factory Tunnel to MagiTek Factory North. If you need to return, take the nearby pipe to be transported back to MagiTek Factory South. There is a save point nearby which you should take advantage of. There is a boss fight that will be triggered when you approach the eastern stairs.
Inferno
Inferno is a three-part boss similar in appearance to Number 128. The central part you need to defeat is Inferno. The larger arm in front (its left) is Striker, and its rear right hand is Rough. Both hands make basic attacks with the occasional special mixed in, and will regenerate after being defeated. Striker's Shrapnel is the most powerful of these, and Striker takes twice as long as Rough before regenerating. If you're going to defeat either hand, defeat Striker. Note that all three parts of Inferno have different weaknesses, and an element that one is weak to will heal another. Striker is vulnerable to Fire and absorbs Ice, Rough is vulnerable to Ice and absorbs Thunder, and Inferno itself is vulnerable to Thunder and absorbs Fire.
Unlike in the battle with Number 128, defeating one hand may not be the optimal strategy. If both hands are present, Inferno will use Delta Hit to cause unavoidable Petrify to a Character approximately every 30 seconds. This can only be prevented with a Relic that grants immunity to Petrify. Inferno will attack with Bolt 2, Atomic Ray, Giga Volt, and Shock Wave. Giga Volt is the most dangerous of these.
As long as either hand is defeated, Inferno will turn things up and use either Bolt 3 or Meteor. Both are nasty, with Meteor doing over 1,000 damage to the whole party. It's up to you to decide if dealing with Bolt 3 and Meteor is worth it to avoid Delta Hit and one hand's attacks. Since Inferno is vulnerable to Thunder and has only 30,800 HP, the optimal strategy may be to simply ignore the hands and use Bolt 3 to defeat Inferno directly. Note that if you defeat both hands, Inferno will use TekBarrier to give itself Safe and Reflect. It will also counter 1/3 of all attacks with the powerful Sobat special regardless of the state of its hands, another incentive to hit it with a few quick, powerful attacks.
Defeating Inferno simply allows you to pass to the next area, but you may want to save again before you leave. When you exit to the southwest, you'll find yourself on the left side of the Double Path. The left side (and only the left side) of this path is one of the few places where you can encounter a Land Worm, which are the only Monster in the area. These giant creatures use Magnitude8 primarily, sometimes using Lode Stone to quarter a target's HP or Compress for significant damage. They are vulnerable to Ice, but you can't run from them.
You will emerge back Outside in a new area. You'll see two chests, but one is blocked by conveyor belts going the wrong way. The eastern chest contains a Megalixir. You'll see a door to the south. Near it is an open chest with a shining red point within it. Inspect this to open a pathway for party 1. Head north to collect the Rainbow Brsh for Relm. You'll have to circle back around to reach the door, which leads to the East Single Path, the other area filled with Land Worms.
This path leads to the East Dragon Room, lair of the Skull Drgn. It also introduces a number of dangerous new Encounters that are worth taking note of. Outsiders appear alongside Madams and do nothing but Throw various Weapons. Fortunately they do a lot less damage than other Monsters that can Throw, but nonetheless the damage ranges from about 600 to 2,000 damage, depending on what's Thrown. This damage cannot be blocked and ignores Defense. Outsiders will counter Fight with Shuriken, and will counter anything else with either a Ninja Star or a Tack Star. They won't counter a fatal blow, but since they have 8,050 HP and are weak only against Pearl, taking them out in one shot can be a tall order. Wound-causing Spells can work. After they've thrown five Weapons at you of their own volition, they usually take their own life with Ruin.
Madams are spellcasters with a huge arsenal of spells at their disposal. They can open with Pearl, Flare, or Imp before spending two turns using support Magic (Cure 2, Life 3, and Safe). They'll then widen their list of support Spells and start casting tier-3 Elemental attack Spells in tandem with them. They may also counter attacks with Cure 2 and/or Meteor. They have similar HP to the Outsiders but the opposite weakness—Madams are vulnerable to Poison. They are also immune to Wound, though vulnerable to many other Statuses.
Retainers appear alongside Hemophytes and are not a big problem in life. They mostly stick to basic attacks, sometimes attacking twice in a round. Every fourth round they may use Wind Slash. However, when you kill them they will use Tradeoff to return the favor. If you have any Characters that are immune to Wound, try to have them finish off Retainers. Hemophytes can attack or use ChokeSmoke (which has no effect), and use CursedGaze as a counterattack to inflict Seizure. If you defeat the Outsider first, leaving the Hemophyte alone, it will start using Shock Wave up to three times per round.
You'll sometimes encounter two Dark Forces, or more often a Dark Force accompanied by two Retainers. These are interesting opponents, more of a gimmick than an actual foe. They use one of three Lores each turn, as well as a few abilities that were perhaps intended to be Lores at some point. The only Lores they cannot use are CleanSweep, Big Guard, ForceField, Pep Up, and GrandTrain. They are the only Monster other than Goddess that uses Quasar, so if you want Strago to learn ForceField from Doom he'll need to learn Quasar from a Dark Force. (Or you can have him fight one boss, leave the dungeon, put him in a different party and fight the other, but that's pretty extreme.) Unfortunately, Dark Forces don't get to Quasar until the seventh turn, and even then there's only a 1 in 3 chance it gets picked. There's the same chance they'll use Exploder right before that turn, too. Learning Quasar from a Dark Force takes patience.
The Skull Drgn
Like most of the legendary dragons, the Skull Drgn has a pretty straightforward strategy. It can use Condemned, Elf Fire, Specter (which inflicts Muddled), and normal attacks for the first four rounds of its cycle, which will be followed by Disaster before repeating. It sometimes counters with a basic attack. And that's it. The Skull Drgn is undead and predictably weak against Fire and Pearl. Ribbons will protect against its Abilities' various Statuses, but the Skull Drgn should fall before any become a major issue unless you have terrible luck. It drops the Muscle Belt, a Relic that increases the wearer's HP by 50%.
With the Skull Drgn dead, you can move on to the Double Switchback and from there to Grand Hall South, an area mercifully absent of Encounters. Walk up and stand on the switch at the north end of the eastern hallway. You're done with party 3, so it's time to switch to another party.