Instructions
Allow the Dark Elf to kill your party in the first fight. There is no sense in even trying to fight back in this battle because you must die to initiate the cut scene. Wait for the scene to finish and the barrier against metallic equipment is lifted.
Take the opportunity to equip metallic equipment on your party. You are given the chance to do so once the cut scene is over. The most important piece of equipment is the Legend Sword for Cecil.
Finish re-equipping everyone's metallic equipment and go up against the Dark Elf again. When the battle starts, have Tellah cast Weak on the Dark Elf. This was the name of the spell in the original SNES version. Depending on the version you are playing, the spell may be called "Wind" or "Tornado." If you have a spell with either of these names, use it before attacking.
Have Cecil attack the Dark Elf. Tellah's spell should have weakened it enough for you to kill the Dark Elf with a single strike of the sword.