Ereshkigal and Areonite?

I'm still on my first play through of Lightning Returns, and I've reached the extra day. I wiped out every species of monster in the world that can be wiped out by day 11. So the Ultimate Lair was a cake walk with one beasty to fight on the way down.

But then I got to Ereshkigal, and I'm stumped. My standard build proved useless. I looked up the Player's Guide's recommended build, and its not doing me much better. It doesn't help that I missed the Chaos' Revenge sword. I had no clue that it appeared on the bridge behind you after the fight with Caius, so I just hopped on my Chocobo and rode off. Hope to get it in New Game+, but for now, I must do without.

Does anyone have any suggestions on how to take these things on? I'm not making a dent in their health bars. And I've completed all but 3 quests (The Girl Who Cried Wolf, Last One Standing and What Rough Beast Slouches). So I'm as powerful as can reasonably be expected on play through 1.