You should do this multiple times while working toward your 25 ranked wins. Following the steps below will make this an easy achievement:
When you start, choose the minimum number of destination cards, preferably short ones or ones that are close to each other. 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 to connect your destinations. Once they are connected, focus on placing the rest of your railways as quickly as possible to end the match. Once your train count drops to 2 or below, everyone takes a final turn and the match is over.
This achievement can be unlocked in any game mode and on any map. It will unlock once the final scores are displayed after the match.