I had some trouble with this battle, but it only took me 3 tries. You have to turn your booster on during the battle with Elly, make sure you have some Frame HPs to use to restore your gear's health, too. The trick is to hit her with X attacks until you get up to attack level 3, then use your best attack, and heal with Frame HPs. Make sure you keep your booster on, that usually defines the outcome of the battle.
Xenogears is the greatest game ever created, by the way. I just found the copy my friend loaned me today and I started playing again. If you think those bosses are hard, just wait till you get to the second disk. There's a boss that decreases everyone's health to 1 at the beginning of the battle.
That game has some sweet moves in it though...just wait till Citan gets his sword
