This achievement must be unlocked on LIVE, although it can be in either a Player or a Ranked match. For maximum efficiency, I recommend doing it in a Ranked match so it counts toward your 25 wins.
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 44 cards. Once you have enough cards, start placing railways across the top of the map so that you connect all of the Canadian cities. After that, simply place the rest of your railways as quickly as possible to end the match.
The achievement will unlock after the final scores are displayed.