The Tower of Fanatics is an interesting place with unique Monsters and a unique mechanic: only Magic works here. You can also use Items, but all other commands, from Fight to Sketch, are disabled. Strago cannot even use Lores here. (Because they are considered Magic, summons do work.) Umaro will still attack as normal, since he doesn't use Commands at all. Further, the Encounters in the Tower of Fanatics yield no Exp or GP, but large numbers of Magic Points. If you want to teach Characters spells without fear of wasting level up bonuses, this is the place to do it.
Several of the Monsters in the Tower of Fanatics have an automatic Reflect effect, and all of them cast powerful Spells. You'll almost certainly want to bring Wall Rings for every Character, both to protect your party and so you can bounce spells off of them onto similarly protected Monsters. A few Spells can pierce Reflect, and you'll want to prepare for those as well. Wound protection is useful against Demi, Quartr, W Wind, and X-Zone. There's nothing you can do about Osmose or Drain except perhaps to respond in kind. You can cast Float outside of battle to protect against Quake. Merton is potentially the most dangerous Spell you'll see in the Tower of Fanatics, so make sure you have Fire protection (e.g., from Flame Shlds or Ice Shlds).
When choosing a party, keep three things in mind. First, Mag.Pwr is the most imporant Attribute for dealing damage here. Second, Weapons and Armor should be chosen for their ability to defend against magic or boost Mag.Pwr, which tends to favor Characters that can use mage-specific gear. Defense is meaningless here, so equip your characters for Mag.Def and MBlock% primarily. And finally, you'll want someone to know Life 3 before you fight the boss at the top.
The thieves at the Base of the Tower give information about the nature of the Monsters here. The one in the middle asks for 100,000 GP to tell you about a secret treasure. He'll tell you about the Ancient Castle beneath Figaro Castle, and also mention that the man in the Narshe Weapon Shop was looking for you. Valuable information, though maybe not 100,000 GP valuable.
The Lower Floors
The entire Tower of Fanatics consists of the same repeating floors and staircases, all the way up to Top above the 38th floor. There are occasionally Treasure rooms to break up the monotony. On the lowest set of floors, you'll find L.10 Magics, L.20 Magics, L.30 Magics, L.40 Magics, and Magic Urns. Throughout the Tower of Fanatics, every "L.## Magic" enemy always has HP equal to 100 times the listed "level." Their actual level is unrelated to this number.
L.10 Magics are tiny undead wizards that attack with the tier-1 Elemental Spells and counter by casting Slow, Stop, or Haste. They have the usual undead vulnerabilities to Fire and Pearl. They appear with L.20 Magics, little yellow-robed wizards who have no Elemental weaknesses and are protected by Reflect. They cast Demi, Quartr, and X-Zone, all of which ignore Reflect. Their counterspells Muddle and Rasp will be reflected, and they also inexplicably counter with Safe from time to time.
Trios of L.30 Magics, green-clad dancers, will use tier-2 Elemental Spells. They are weak against Poison and have no inherent defenses except the ability to absorb Pearl. They can cast Rflect as a counter, though, so try to avoid queuing up multiple Spells on them, or just bounce them off of your own Reflect. They can also counter with Osmose, which is especially annoying in this place.
The highest-level Monsters in the area are L.40 Magics, green floating men with a vulnerability to Thunder who appear with L.20 Magic allies. Like L.20 Magics, L.40 Magics can cast a Reflect-piercing Spell, in their case Drain. This can deal significant damage if the L.40 Magic has been hurt. They can also counter with Mute or Sleep, neither of which will get through Reflect.
Finally, there's a rare encounter against a pair of Magic Urns. These appear with more frequency in the various Treasure rooms in the Tower. They are helpful creatures that will bring Wounded Characters back to life with Life or Life 2, remove Petrify with a Soft, or use a Remedy or Tincture on a random party member. After any such action they have a 1-in-3 chance to run away, but if you're lucky and they stick around they may us Potions, Ethers, or even Elixirs on your Characters. You'll get 5 Magic Points whether you defeat them or they run, so let them do their thing and reap the benefits.
As you climb, you'll spot a door on the eighth floor. This Room contains a chest with a Safety Bit. Like most of the Treasure rooms in the Tower of Fanatics, the encounters here are different than those outside. Magic Urns are more common, but you can also run into a L.50 Magic or L.90 Magic, so be careful and don't dilly-dally.
This particular Treasure room has a secret two thieves in Maranda hinted at. Investigate the wall right of the chest, and you'll hear a sound. This opened a door on the floor below. The 7F Room contains not only Edgar's rarest Tool, the Air Anchor, but you'll also exclusively find Magic Urns here.
The Middle Floors
When the screen changes, you'll be greeted with a new set of encounters. You'll sometimes see a team-up between a L.10 Magic, L.20 Magic, and a L.30 Magic, but most of the Encounters in the area involve new, higher-level Monsters. L.50 Magics are undead demons that are vulnerable to Fire and Pearl. They cast Doom,Poison and Bio, none of which will bypass Reflect. They will counter with Slow, Haste2, or Bserk. This one of the few ways you'll see anyone make regular attacks in the Tower of Fanatics. Bserk is useful for shutting down a Monster's spells, but the Monsters here all have high Defense so it's not a great offensive strategy.
The final Encounter, other than the rare Magic Urn encounter that is found on all floors, is with a L.40 Magic, a L.50 Magic, and a L.60 Magic. L.60 Magics are humans dressed as cats, and the first legitimately dangerous Monsters in the Tower of Fanatics for a party equipped with Wall Rings. They cast Quake, which deals thousands of Mag.Def- and MBlock%-ignoring Earth damage. Make sure you have Float on whenever they are a potential threat. They can also use W Wind, another Spell unaffected by Reflect. Their least dangerous attack is Pearl. They can counter with Osmose to drain your party's MP, as well as both Slow 2 and Regen. They are vulnerable to Fire and absorb Ice.
The 17F Treasure Room contains a Genji Shld and the normal Treasure room encounters with L.50 Magics and L.90 Magics in addition to Magic Urns.
Once you reach the 21st Floor, you'll start to Encounter L.70 Magics. These burning demons use tier-3 Elemental attack spells and counter with only Reflectable Spells, and as such they are actually less of a threat than some of the lower-level Monsters. They do have a permanent Reflect effect, though, so don't target them directly. They are vulnerable to Ice and Water.
The 26F Treasure Room is the most interesting so far. In addition to the Stunner, Shadow's best Weapon, you'll find the White Drgn wandering around in here.
The White Drgn
All the White Drgn does is cast Pearl over and over. If you have Reflect, this will result in it healing itself with Pearl-Elemental damage, but it's better than your party taking damage. The White Drgn will counter Magic by casting Dispel, presumably in an effort to remove Reflect. However, the Reflect Status given by the Wall Ring cannot be removed, so this is futile. (Dispel will remove Float though, so be sure to reapply it after the battle.) All in all, the White Drgn can't harm a Wall Ring-equipped party at all. It has no specific weaknesses, so use your most powerful non-Pearl Spells, perhaps reflected off your own party for extra hits, and it should fall in no time. You receive the Pearl Lance after the battle. The White Drgn will appear later on the Veldt, though because the Pearl Lance is not an actual drop, you won't be able to get more of them this way.
The Upper Floors
When you reach the home stretch, you'll finally run into L.80 Magics, which can appear in pairs or alongside a L.90 Magic. These are elegant red-clad ladies that will cast healing and support Spells on your party if they have Reflect. She'll normally cast Cure 2, Remedy, or Haste, but will cast Cure, Cure 3, or Life 3 if she's attacked by someone with Reflect. That's likely all they will do, but if for whatever reason you're not using Wall Rings, L.80 Magics will attack with Bio and Poison. If any of their allies have Reflect (which L.90 Magics do), they'll use a tier-3 Elemental spell on their own party. They'll also use Stop, Dispel, and Pearl as counterattacks against non-Reflective opponents. As humans, they have the typical human weakness against Poison.
L.90 Magics are, appropriately, the most dangerous Monsters in the Tower of Fanatics. They're (somewhat) prepared for enemies with Reflect, and will cast Meteor (which will hit no matter what), Flare (which can be Reflected), or Merton (which will do massive Fire damage to friend and foe alike, and should be protected against at all costs) every round. After three rounds, they'll cast Dispel then up to three Flares in a row. They can counter with Life 3, as well as the less notable Stop and Bolt 3. They have a lot of HP, permanent Reflect, and are protected against Water, Wind, Earth, and Pearl.
The 35F Treasure Room contains a suit of Force Armor, useful Armor in the Tower of Fanatics that offers excellent magic protection. The final treasure is in a Room atop the tower, and contains the Gem Box. Make absolutely sure you are prepared before you take this treasure, though. When you try to leave, you will be attacked by the MagiMaster, whose final Ultima attack will almost certainly wipe out the party. Life 3 is the most straightforward way to survive the battle despite this, though creative players can find others.
The MagiMaster
The MagiMaster can do almost nothing to a party protected by Wall Rings. Unfortunately, "almost" is very much not good enough in this case, as the MagiMaster will cast Ultima for around 6,000 damage per Character when it dies. Unless you have the HP to survive that, make sure to cast Life 3 on at least one Character early in the fight (don't worry, Life 3 won't be Reflected). Don't forget, or you'll lose all the progress you made climbing the Tower!
The MagiMaster's attack sequence is straightforward. It starts with a random tier-2 Elemental attack Spell, then follows that up with a tier-3 Spell. Its attacks will intensify from here, using two tier-3 Spells per round for the next two rounds. Then it levels off with one last tier-3 Spell followed by two Spells chosen from Doom, Mute, or Bio. None of its can bypass Reflect, so the MagiMaster offers no real threat outside Ultima. Note that if you cast Rflect on the MagiMaster for some reason, it will start bouncing tier-3 Spells at you.
Every time you attack the MagiMaster, it will counter by changing its weakness with WallChange. There's no indication what the new weakness is, and it changes with each Spell, so it can be very difficult to consistently damage the MagiMaster. There are two effective options. First, if you have them, you can use the non-elemental Spells, Flare, Meteor, and Ultima. Or second, just don't attack at all and let the MagiMaster kill itself with its own Reflected Spells. As long as you don't attack even once, it won't use WallChange and will remain vulnerable to every element. It's not very exciting, but it works. Just don't forget to cast Life 3! The MagiMaster drops one of the two easily obtained Megalixirs in the game.