I've been looking at strategies for the burgerfight, and they seem to have a theme of either overpowering your characters way past the level 37 that characters will tend to be by the end of BT1 (One strategy depended on a level 67 party to make the Travellers tune powerful enough to lower the AC enough), or by designing a party well outside of game norms (4 monks, a bard, and two wizards).
So I worked out a strategy to win both burgerfights that, despite using kind of strange Bards Tale game features, does use a conventional party design of a Monk, a Paladin, a Warrior, a Bard, and three Wizards.
fight preparing 1) Give your spectre snare to your paladin, 2) Put dragonshields in your inventory (3 will do, but 4 is better) 3) Bard song: Travellers tune and contingency spell YMCA 4) order your party as follows, Monk, Paladin, WIZARD, WIZARD, Warrior, Bard, Wizard, yes, I am telling you to put the wizards in the fighting line.
Fight #1 Round 1, Your bard plays travellers' tune because in combat songs ADD to the ambient songs, your rank seven Wizard casts anti-magic.
The monsters wither and kill your mages, your monk and Paladin survive (your monk may have taken some damage from Jabberwock breath.. but now the anti-magic is up, no more damage will be taken), your front wizards die, and MOVE TO THE BACK, putting your warrior and Bard into slots 3 and 4, now that their AC's are low enough to not get hit thanks to the Bard songs..
Your front line is now solid, good, you'll need it..
now you heal your wizards, and use spells, it only takes a couple WIZW to kill each group, and you win the first fight...
AND NOW THE SECOND..
Ok, two of your wizards are withered, and this kills their saving throws, you lose your contingency spells, this really sucks. So..
Round 1, You have your paladin defend (very important), with the defend her AC is low enough to not get hit, her luck bonus means she wont take spell or breath damage... you have your Non-withered mage (who is now in space 5) cast "Invisibility", to drop her AC... and everyone else probably dies... maybe your Monk survives, but not much longer..
Round 2, your unwithered mage dies, and your Paladin starts dragonshielding...
Your paladin now has an AC of -43, she will not be hit, her Paladin luck bonus means breath and spells wont hurt her, now she dragonshields every round... BUT THERE IS A CATCH..
The game only allows four groups of enemies, but if you kill one group all the way, the summoners (Demon lords, Balrogs, liches) will summon more, so what you must do is dragonshield the most numerous group every round until you've whittled it down, equip a new dragonshield when the old one is spent (remember I said have three), and carefully whittle it down until you win and get your paladin a million or so EXP's..