I was able to do it with a level 99 Chaz, Algo Ring, Elsydeon, and Psy Mail, and a ton of save state abuse. Chaz has 635 HP, so he needs to be able to hit Re-Faze twice between Sol Dews. That means Megid can do no more than 211.33 damage per use.

After a certain point, you can begin to alternate healing and damage dealing. The following figures are for after using the Power Shield. Crosscut does around 515 per use, and there are 39 charges, adding up to about 20,085. Re-Faze has 32767 HP, so you need to deal the remaining 12,682 damage by attacking, Rayblade, or Airslash, all of which do about 415 on average. That comes out to 31 attacks.

You will need the three vehicles, Aeroprism, Rykros Ring, Power Shield, and Swift Helm (not strictly necessary, but strongly recommended). You can give the Psycho Wand to Rune or Raja. Fill the other 33 spots with Sol Dew. Chaz has enough TP to cast Nares 40 times, but once you run out of Sol Dew, you'll need to use Nares two out of every three turns to keep up (and the healing from 3 Nares must exceed the damage from 2 Megid). So, you get 53 heals, and you need to deal damage 70 times. That means that you must survive 3 uses of Megid without healing 18 times. It could hypothetically be done on a cartridge, but I wouldn't recommend trying.

Also, there's something I am having trouble understanding: based on my understanding on how magic defense works, the Reflect Mail should be far superior to the Psy Mail in reducing the damage from Megid, but it doesn't seem to be (though I haven't tested it extensively). Can anyone here explain exactly how this works?