This is story-related and can't be missed.
During your journey to ring both bells you'll probably step into the forest area of the game, Darkroot Garden and its lower counter-part, Darkroot Basin. To acquire the 'Art of Abysswalking' means you'll have to acquire the ring called 'Covenant of Artorias' that allows you to reach another area of the game - the Abyss.
To get the ring you'll have to beat the boss Great Grey Wolf Sif that is located in the upper part of the forest, behind a sealed door. There are two ways to reach this boss, one is to buy the crest that opens this sealed door from the Blacksmith in Undead Parish (for 20.000 souls) which will allow you to pretty much run straight to the boss door. The other method is to take the long way around going all the way down to Darkroot Basin, defeating the 'mini'-boss Hydra that sits in the lake and then proceeding to take the ladder right next to it, reaching the locked area of the forest and the boss door, which you will still need the crest to open anyway.