TIL That you can skip the Taurus Demon and fight the Gargoyles at the very start of the game.

You must have the master key to do this. All you need to do is go to where you enter Blight Town through New Londo Ruins. Instead of entering the tunnel, go to your left and start running. You will come to a bridge and the Undead Dragon. Do not pick up the Shield and the dragon will not wake up. Now all you have to do is dodge the drakes and take the elevator to Darkroot Basin. If you are lucky the black knight will jump off and die. Now just take the way back up and you are at Andre. Also you can walk on the bridge and the dragon will not spawn until you do the scripted event in Undead Burg. I found this out while trying to do my SL1 Darkwraith character and I wanted to get my Battleaxe + 5 quickly. I am not sure what will happen when you enter the Taurus Demon's area from the other side.