This article is from the Final-Fantasy and other Square Soft Games FAQ, by email@example.com (Nick Zitzmann) with numerous contributions by others.
Before you even enter Cave Magnes, you **must** have the TwinHarp in
your inventory. If you don't, you'll lose every single time. (You can
get the TwinHarp by finding Edward in Toroia Castle.)
If you have the TwinHarp, though, after you lose the battle to the Dark
Elf, Edward will start playing his harp, which will be broadcast through
the TwinHarp and distort the magnets inside the cave. At this moment,
you should re-equip all of your characters with their regular weapons
Now, the Dark Elf should be easy for the party to demolish. Still having
trouble? Hint: The Weak spell works against him.