To unlock this achievement, all of your routes have to be connected in some way. They do not need to be a continuous route, you can have dead end branches and still unlock the achievement. You can easily earn this using the method detailed below:
When you start, choose the minimum number of destination cards. Your partner will take the minimum also, and every turn will choose just one destination card until he runs out and then switch to drawing railway cards. You will focus on drawing railroad cards, always drawing two face down cards until you have 60 cards. Once you have enough cards, start placing railways, always placing them starting at a city you already have a rail running to (other than your first move, obviously).
This can be unlocked in local play or on LIVE. The achievement will unlock after the final scores are displayed.