Walkthrough

You know the drill by now. When you're ready for the final battle, talk to Matelite!

OK, we've got four heads to beat (all of which have infinite MP, in case you're wondering). The upper right one is the healer; the upper left one does dragon spells like Ice Breath; the lower one does status effects, and the middle one does Summons(!). You can't hurt the middle one until you've beaten all three of the other heads, but once you do beat the middle one the battle's over. Mini-Devils are a definite no-no for this fight, and you shouldn't use Assassins either. Stick with tried-and-true: two parties with a Cross Knight, a Knight, a Heavy Armor, and a Light Armor; one with four Wizards, one with four Priests, one with two Summoners and two others (doesn't matter since you won't be using them in melee fights at all, but you'll be left with Lancers so you might as well use those); and the last would probably also be good to have Matelite, a Knight, a Heavy Armor, and a Light Armor.

At the start of every phase, go through your units and use Heals, Litancibles, and Magic Gins if you have to, and use one or two Royal Drugs (or four or eight High Drugs) if you're nowhere near a good spot to be hit by a White Drug from your Priests. Keep your parties at or near maximum HP at all times. Also, if you beat a head, be sure to equip any good items you win on a character (and you can win some great items, so save and restart if you don't get a good one).

Start by getting rid of the top right head (at X19 Y05). It has the least HP and it's the least dangerous. After that, go for the upper left head (X11 Y06). It'll take a while, but you can beat it. While you do, though, keep your party as far away from each other as possible, since the middle head's Summons can do nasty damage to many characters. You'll actually be using your Priest party in this battle, unlike most of the previous others. Once that head is gone, head to the lower head (X09 Y14) and start hitting it. The lower head is actually the least nasty, since its status effects are easily countered by using Heals in the Party submenu, but eh. Your main problem during this time is that your dragons will be targeting the middle head even though it won't do any damage! Once the lower head is gone, spread out your magic parties and go in close with your physical parties to attack the middle head (X10 Y10). It has 50,000 HP, so it'll take a while, but if you keep healing yourself with items, you shouldn't have any problems. Since it'll only get one turn per phase, you shouldn't lose any of your units. When the final head's gone, sit back and go with the flow for the ending! Congrats!

But we're not quite finished yet. ^^; If you like, once the ending is over, return to the start screen; there's a new option, Ex-Play. Similar to New Game+ from Chrono Trigger, you can pick a saved game (here it would be your chapter 27 game) and you can start with your characters and dragons at the stats they were at that savegame! You'll also keep all your money and items. There's an extra option, too, in the Inventory menu: you can now see what the effects of each item would be if you fed it to a dragon. Finally, your Summoners can summon Alexander right from the start of the game (it absolutely rocks). You may want to give the Hard Dungeon a try as well!