WarMECH
WarMECH appears in 4.7% of encounters on Floating Castle 5F. You probably don't want to see it on your way to TIAMAT, but WarMECH is worth a whopping 32,000 Experience and 32,000 G if you manage to destroy it, so you may well come back to hunt it later. Truth be told, there are more efficient ways to earn Gold and Experience, but this is arguably the ultimate challenge in the game, so you will want to test your mettle if nothing else.
Finding WarMECH is easy, though potentially time-consuming. None of the other encounters on this floor are particularly dangerous, and you can run from any of them with ease while looking for WarMECH. Be aware that WarMECH usually gains surprise. Its attacks are nasty, and there isn't much you can do to blunt them anyway. Your best defense here is, as the saying goes, a good offense.
WarMECH has two forms of attack. Its physical assault deals more damage than any other attack in the game, and it gets two of them. Even your KNIGHT will take damage well into the triple digits from one of WarMECH's attacks. You can try FOG2 or INV2, but they won't make much difference without repeated castings (which you don't have time for).
The bad news is that its special ability, NUCLEAR, is even worse. Fortunately it will only decide to use it 1/4 of the time. NUCLEAR deals at least 80 damage to each Warrior even when it "misses", and there's no guarantee that it won't pierce your Magic Defense and deal up to quadruple that amount. This attack is non-elemental, so neither Ribbons nor spells will help you cut down its damage.
Since you can't do anything about WarMECH's attacks, you should focus squarely on offense. It resists every relevant element and has extremely high Magic Defense, so physical attacks are your only recourse despite its 80 Absorb. Its Evade is slightly higher than TIAMAT's, but it has the same 1,000 HP, so you can expect your offense to be similarly effective against WarMECH. That said, BANE is not an option here.
As with TIAMAT, a MASTER is effective here because their large number of hits and high critical hit rate give you a good chance to bypass WarMECH's Absorb. Weapons like the Masmune and Xcalber are also very effective for the same reason. You are very likely to lose at least one Warrior during this fight, so throw everything you have at WarMECH. Even if your EXIT casters fall, you can warp out of the dungeon via TIAMAT's room (assuming you've already defeated her, at least). Good luck!