Fun little challenge build. Not difficult by any stretch.
Only level strength to 20 and don't upgrade anything.
Notes:
Grab the Claymore on the Hellkite Bridge; that will carry you to the depths unupgraded easy until you meet Domhnall of Zena.
You won't be leveling, so use your souls to buy multiple Crystal Greatswords.
A single Crystal Greatsword should hold out until Ornstein and Smough before it breaks.
DON'T pick up the Lightning Spear in Sen's Fortress or the Occult Club in Anor Londo. These count as +10 & +5 weapons respectivley and you'll be paired up with invaders accordingly, unless that is your intention.