Well I have finished Dark Souls with a lvl 102 mage and I can tell you the big reason why I was able to is I found a way to grind lvls in the game.
For those who don't know MINOR SPOILER DON"T READ BELOW IF YOU WANT NOTHING SPOILED.
When you reach the first blacksmith in the game there is an item you can buy I think its called crest of Artories or something like that it cost 20k souls to buy. Pick this up as soon as possible. If you go into the forest area and stay on the main path you will run across the door it opens, if you hit the wall to the left of that door you will find a hidden bonfire. The enemies behind that door give you 1k to 2k souls per kill and you can reset them by hitting the bonfire so you can grind souls easily.
An easy way to get 20k souls to buy the item starts at the second bonfire in the main game or the first in undead burg. When you go below the bridge the red dragon is guarding and kick the ladder down, simply come back up make the dragon mad...
If it's a 10 hour game (or less) I can see that. That's a little more than an hour a day. Though a huge game like Dark Souls is a bit strange to finish in a week. Sounds like it'd take some major free time to me.
Maybe if you're the world's greatest gamer, and you have a hell of a lot of time, maybe. I don't follow Dark Souls, but it sounds like one of those big games that lasts a long time. If you can finish a game that an average person might beat in a month, you deserve a metal and to achieve enlightenment.
It is possible to beat the game in a week. The other day I finally got the chance to put some serious hours into it, and in a time frame of three hours I obtained all the items in Blighttown, killed Blighttown Boss (Queelag) explored two other areas and got some decent leveling. If I had kept playing I would've been in Sen's Fortress and probably gotten through that as well. All in one day.