This is obtained by defeating Pinwheel, the boss of the Catacombs. Having a divine weapon to reach him is almost a must given the otherwise continuously reviving enemies on the way (though killing the undead mages does help this as well, you're really best saving yourself headaches by bringing a divine-enchanted weapon.)
Pinwheel himself is actually a pretty easy boss comparatively speaking, as he doesn't have a tremendous amount of health and if you pay attention you can dodge his primary attack--slow to charge straight-line projectiles--with relative ease. The tricky part of the fight is that he will begin to clone himself and randomly teleport around the area--with each clone starting to shoot off the same attacks as well.
Try to knock out the clones anyways (they should drop to a hit or two from a divine weapon)--and keep an eye out for the one doing the 'clone more of myself' animation to pick out which one is the real Pinwheel. Once he's down, you'll get the Rite of Kindling which helpfully allows you to kindle bonfires for even more Estus flasks in tough areas.