Is there a shortcut to the Executioner's Chariot?

Solution 1:

There isn't a shortcut of any kind, unfortunately. Sorry. Confirmed in the Collector's Edition game guide.

As for the Chariot, it's really not that difficult of a fight relatively speaking. If you want some tips, see below.

As soon as the fight starts, begin heading to the left. There are skeletons that will harass you, but don't worry about killing them. They will be resurrected by one of two necromancers. Basically, just push around the area as much as you can, taking time to duck into the small alcoves when you see the chariot coming. The chariot will either kill or knock down any skeletons that happen to be harassing you. Keep sprinting toward the first necromancer and kill it. Then clean up all the skeletons around you. Next sprint toward the second necromancer and and kill it, then clean up the skeletons. Once the two necros and all the skeletons are dead, you should see a switch across from you. Flip the switch and the fight will transition into a much more traditional style boss fight. Good luck and remember that horses don't like it when you stand right behind them.

Solution 2:

If you go from the third bonfire, there is a bit of a shortcut. But you will have to do a pretty fancy jump. It's surprisingly easy for how it looks. What you do, is from the third bonfire, go to the left side of the bridge you lowered to get there. Stand on the very edge, so you can see the edge below. Run along the edge, and jump against the very edge of the wall. You will be pushed slightly to the side, but you will keep going straight, and land on the edge of the ledge below. Try to spam rolling to the left when you land, so that you don't accidentally fall of while turning or something. The trees down there will not have loaded in yet, so don't be starteled when they suddenly appear