After defrosting the Frozen Eleum Loyce, you can enter the Old Chaos and fight the ultimate badass of the Ivory King DLC: the Burnt Ivory King. If you come prepared, this fight won't be too challenging. Otherwise, prepare for a hellish battle.
What do I mean by "prepared?" Once the blizzard stops in Frozen Eleum Loyce, you should explore the new areas that have opened up. This will introduce you to three Knights of Eleum Loyce, essential to defeating the end boss. Once you've found all three, you can safely proceed.
When the battle begins, you'll have to dispatch a bunch of soldiers that enter through chaos gates--this is why you need the Knights. One by one, they will sacrifice themselves to seal the gates, preventing more soldiers from spawning. After a few kills, the Burnt Ivory King himself will arrive.
His attacks are simple--lots of sword swipes and combos. Roll or block these to prevent damage, no problem. He may also plunge his sword into the ground before him. Keep back to avoid the energy that pulses up.
After a while, the King will buff his sword. The fight proceeds as usual, though his sword is now much, much larger and does magic damage. Continue to dodge until the sword debuffs, and you'll have no problem.
The Burnt Ivory King may seem intimidating, but the fight is simpler than it appears. Bring Knights to seal the gates (seal the boss in one for an instant kill!), watch the King's sword attacks, and you'll take him down without much difficulty.
For more help be sure to check out our complete Dark Souls 2 Boss guide.