Continue your journey with Prima's Dark Souls 2 Guide and Walkthrough!
Approach the Invader with extreme caution. It has all of the same abilities as your character, as well as a longer reach. Wait for an opening to attack, then get around behind it for a critical hit. This is the easiest way to inflict massive damage and finish it off quickly.
With the Invader down, head back to the bridge and jump over to the item to find a Sublime Bone Dust and a Fire Seed. Jump back over and head into the mist ahead to battle the Executioner's Chariot.
Reward: Executioner's Chariot Soul
The battle against the Executioner's Chariot is unique in that you don't immediately fight the chariot. Instead, you are presented with a longer, curved corridor. Various Skeleton enemies inhabit the corridor, but they are not the primary concern. The chariot takes up the entire corridor and races through the area in a circular path. It passes your location about every 10-15 seconds. The only way to avoid the chariot is by ducking into one of the small alcoves along either wall.
At the onset of the battle, ignore the enemies and run ahead, keeping a close eye on the alcoves so you always know where to find the closest one. As soon as you see the fire from the chariot, duck into the closest alcove. Continue this process as you make your way down the corridor. If the Skeletons are in the way or become too much of a problem, you can take them out, but always be mindful of the chariot's location.
When you get close to the end of the corridor (where there's a large hole in the ground), you will see a door blocked by mist on the left. Just before you reach the door, there's also a lever on the left. Pull the lever to lower the gate ahead. When the chariot hits the gate, it crashes, killing the Executioner. This leaves you to battle against the horse that pulled the chariot.
Always stay to either side of the horse. Never stand in front of or behind the horse to avoid the main attacks. When the horse stands on its hind legs, dodge to either side to avoid the stomp attack that follows. You also need to dodge to avoid the head butt attack that comes after the horse pauses for a moment. Both of these attacks inflict significant damage even if you're attempting to block.
Occasionally the horse sprays a dark mist from its mouth. This is the best time to attack from the side as the horse moves slowly to the left or right in an effort to hit you with the mist. Stay at its side and attack relentlessly to inflict as much damage as possible.
Once the Executioner's Chariot is down, finish off any Skeletons that are still alive and pick up remaining Fading Souls. Walk to the end of the corridor to find a Soul of a Brave Warrior, then head through the doorway that was previously blocked by the Mist. Go down the corridor and up the stairs, light the bonfire on the left, then speak with the man just ahead. This concludes your adventures in the Undead Purgatory for the time being.