The right path
Turn right at intersection, and you'll have to battle two enemies, both of whom are invisible.
The first is standing in plan (invisible) sight behind a turret on the left side of the path. Like all invisible enemies in Dark Souls 2, he's technically more translucent than invisible. As long as you know you're looking for someone, you should be able to identify him.
Before you fight him, pillage a corpse on the right side of the path for Prism Stone x 15. Then walk behind the turret and get the first hit in, aiming for the spot where someone just about to use the turret would stand.
If you have a weapon with a wide slash swing like the Dragon Tooth we use in the video, equip it. Because you can't lock into your invisible foe, a slash move lets you cover a lot of space and makes it easier to connect. If you lose sight of him or need health, double back the way you came to get your bearings and drink Estus in relative safety. He can use Estus, too, but that can actually be to your advantage. When he drinks, you'll be able to identify him by the floating bar of HP that appears above his head. Seek and destroy.
Put your guard up and make your way toward the second turret, behind which another invisible enemy is hiding. Pillage two corpses for Goldenfruit Balm x 2 and Large Soul of a Brave Warrior x 1 and then walk behind the turret waiting for your invisible enemy to strike. Take him down using the same techniques that you used with his buddy.
This path dead ends with a Pharros' Contraption. Like many other things in Crown of the Ivory King, it's covered with ice. There's nothing you can do with it now, so just file its location away for later.
The left path
At the T-shaped intersection, turn left, away from the path that leads to the Pharros' Contraption. In the middle of a covered structure, kill the Sorcerer inside the door to your left. Inside that room, pull the switch to activate the elevator, and you'll see a platform containing a bunch of coffins rise. That is, in fact, the same platform you saw on the path between the first and second bonfires. We'll double back soon.
Exit the room, turn left, and then turn left again to kill a Rampart Golem. Right before the staircase, pillage a corpse for Green Blossom x 8. Double back the way you came, passing the hallway on your right, ascend the stairs and open the door where you'll fight five Frozen Dogs. They're aggressive, so you can back up the winding staircase next to the door and, if you're lucky, take four of them down as a pack. A fifth will descend the staircase and shouldn't pose much trouble.
Head to the wall opposite the door and pillage a corpse for Human Effigy x 1.
Walk up the staircase and out the door on your right, where you'll find a corpse to pillage for a Soul of a Great Hero x 1, which you can squeeze for 20,000 souls.
As you exit the balcony, kill the approaching Sorcerer.
Exit the room and follow the path ahead down the staircase, where you'll fight another Rampart Golem with a lance and a shield. Kill him and proceed through the doorway at the bottom of the staircase.
Hop down the ledge over the missing stairs and pillage a corpse for Crimson Water x 1.
Continue down the path, listening to the disembodied voice's warning as you go. Ascend the staircase to the right of the structure at the end of the path and pillage a corpse for Eye of the Priestess x 1, an item that will make your upcoming fight with Aava, the King's Pet much easier.
Head back down the stairs, turn right, pass the locked door on your right, and head down another long, shallow staircase, where you'll have to fight an Elite Knight.
Continue down the path, turn right and pillage two corpses just before the next staircase for Alluring Skull x 5 and Skeptic's Spice x 1.
Enter the mist in the doorway at the the top of the staircase, run forward (beware of lingering, or the Retainer down the hallway to your right will fire a sorcery at you) and light the Inner Wall bonfire.