When you are in the lower level of Blight Town, you can get this sword before fighting Quelaag.

Head all the way to the left side of Blight Town lower level until you see a big tree. There will be a root where you can go up into it. There will also be giant leeches in the area so you will know if you are there.

Go into the tree and hit the wall to reveal a hidden path. Get the treasure and then hit the wall again. There will be another hidden path.

I was already pretty strong when I did this so the monsters in this area were easy for me, but if you are a lower level then take caution while exploring this area.

I would suggest you just run away from any enemy until reaching your destination. After revealing the path, go all the way down using caution because you can fall down and die at anytime.

When you reach the bottom, you should be in "Ash Lake". Go to the right and you will see a bonfire, go to the left and you will see a Hydra so be careful.

Run straight all the way towards the end of Ash Lake and you will see the Everlasting dragon. Join his covenant and he will give you the Dragon head and Dragon's eye.

To get the sword, just go right behind him and attack his tail. he will not attack you at all. Cut it a few times and it will break, turning into the Great Drake Sword.