The Ivory King DLC for Dark Souls 2 has one last, evil trick up its sleeve: the Frigid Outskirts. If you can survive this horribly difficult area, you can reach a small grotto and fight the DLC's final, optional boss: Lud and Zallen, the King's Pets.
As I'm sure you've figured out, this boss is simply the previous fight with Avaa, done twice. Lud will attack you first, with Zallen joining in once some damage has been done to his brother.
Use the same strategy as that earlier fight, dodging paw swipes and ice crystals. The tricky part is when both pets are in the fray. At this point, you should avoid targeting one or the other, keeping both in sight. This way you'll know when one is targeting you. Keep a watchful eye, and you'll avoid being cornered.
Lastly, make sure to kill Lud first. When Zallen reaches about 40% of his health, he'll go into a fiery state of frenzy, doing higher damage and slowly regaining his health. As long as he's the only one active, you can stay alive until this buff goes away.
Be persistent and bring friends if you need to (the boss is intended for co-op), and the final boss of the Dark Souls 2 saga will fall.
For more help be sure to check out our complete Dark Souls 2 Boss guide.