Undead Purgatory is accessed from Undead Copse, taking the route towards the ambush of four dark mace and whip-wielding enemies.
Head along the second narrow footbridge from the second bonfire in Huntsman's Copse, the Sickle-wielder might run towards you after you go across the first bridge, kill him if he does. Over the second bridge, kill the two zombies and dark weapon zombie.
Run up the hill and turn left, this is where the four-man ambush lies in wait; walk forward very slowly until the first foe drops down and runs towards you, then kill him. Proceed forward slowly once again, along the left hand side. The second enemy should jump down once you reach the edge of the small ledge. The third will jump down from near the wooden bridge once you move a little further, and the final guy will fall on the right.
If all hell breaks loose, it's better to die here and restart from the bonfire, as you'll be facing a Red Phantom across the bridge and have a better chance of regaining your souls here instead of sprinting like a crazy person hoping to pass through the mist.
Once these four enemies are down, head across the wooden bridge. Move the camera high so you can see the bridge itself; there are gaps in the floor, so watch your step. At the end of the bridge you can jump to the right before the red phantom and grab the item.
Now you need to face the Red Phantom; this guy is incredibly tough thanks to his giant sword and shield coupled with incredible speed. There are few opportunities to counter attacks thanks to his quick recovery rate. For melee characters, your best chance is to look for backstabs. Unlike regular enemies, you can't hit him as he is getting up from a backstab, so don't waste your stamina. If you find yourself in trouble, run back across the bridge, he won't follow you. Heal up and try again.
Once the Red Phantom is down, it's time to face the Executioner's Chariot.
How to beat the Executioner's Chariot
This boss looks tough, but is very easy once you understand the method. First, ignore the chariot, and focus on the skeletons. Once again, they're weak to fire, so use the Fire Longsword if you have it, or fire spells if you're a mage. The Chariot is also weak to fire, so try and save some spells for it if you're a mage.
Run as far as you can left, using the doorways to avoid the Chariot as it passes. Take out the skeletons as they overwhelm, but they'll respawn until you kill the witch doctor found about halfway around the circle. There's a second witch doctor found further ahead, but kill all the skeletons here before proceeding otherwise they'll swarm and kill you.
Once the witch doctors and skeletons are down, keep heading left until you find the lever the skeleton pulled in the cutscene. Pull it and lower the gate. The Chariot will crash and you'll be left to fight the horses. Stick to the side and slash away. The horses will buck and ram, as well as spew dark energy at you, each of which does very high damage - staying at their side lowers the odds of being hit by any of these attacks.
Once the Chariot is dead, head up the stairs and ignite the bonfire. you'll also run into Gren, who will grant you the opportunity to join a covenant if you have invaded and killed at least one other player.