This is a fairly easy boss battle if you know how to proceed with it.
When you first enter the fog gate, you will be placed in a circular hallway with the Chariot moving in a counter clockwise direction. You need to move clockwise in order to activate a lever which will block the Chariot's path. Move counter clockwise, trying to avoid the skeletons as best you can. Use the openings on the walls to protect yourself from being trampled by the Chariot. You will also see two necromancers hiding in two of the openings. Kill them both if you can.
Once you activate the lever, a gate comes down that blocks the Chariot's path. The Chariot crashes into the gate and the real battle begins. This battle quite easy as the enemy's moves are easy to dodge. usually evading to the left or right will suffice. If you stay near its back, it'll do a back kick so you'll need to roll away or block it with a good shield.
Killing this boss gets you 'Exectuioner's Chariot Soul' and 19,000 souls
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The Executioner's Chariot is a boss in Dark Souls II. Located in the Undead Purgatory, the...