Easy Mode
4 AI
10 Victory Points - Standard Game
To win victory points, build settlements, upgrade them to cities, get the Longest Road or Largest Army cards, or build development cards to get Victory Point cards.
You start the game with 2 victory points for your two cities. A common strategy I use is to build them close to one another, but not too close, and connect them with roads until you get the Longest Road card. I then build development cards and use the soldiers I would get from it, while probably getting at least 1 victory point card. Once I get the Longest Road and Largest Army cards, which gives me a minimum of 6 victory points, I buy development cards while building settlements or upgrading cities, and the win comes very quickly.
After 10 games of doing this, you should get the achievement.
TIP: Do NOT do this achievement along with Knight and Builder of Catan. If you are to get all 3 achievements, or any other achievements, simultaneously in this game, it will record one and void all the others unless you load Catan onto another Xbox 360 and recover your gamertag. This is the only known workaround. View Xebu's comment below for more information.