I might be misremembering, but you don't really need to defeat Elith? She's just one of those characters who you're expected to lose to, like Nel and Violet. But it's been a while since I've played, so I might be wrong.
If you do actually need to defeat her, I'd consider: rethinking your Skill and Accessory/Equipment layout. I seem to recall that she puts you to sleep, so, maybe pack anti-sleep potion(s)? And if all else fails, level up some more, perhaps with Nel's help. She sure does make grinding a lot more convenient. Each level up gets you more health, Mana, and damage, so it can't hurt.