This achievement requires that you select and keep all five destination tickets that are presented to you at the start of a 1910 Mega game. The Mega game has more than 60 destination tickets, so many more than a normal game, and some of them can be quite long. Since you don't get to pick and choose, you may have to try this multiple times, but it can be done in local play with a second controller or on LIVE with a partner, so the only barrier to success is having enough trains.
When you start, choose all of the destination cards offered. Your partner will take the minimum, and every turn will choose just one destination card (there are so many he will not run out the entire game). You will then focus on drawing railroad cards, always drawing two face down cards until you have 60 cards. Once you have enough cards, focus on placing your railways as efficiently as possible to get all five of your destinations completed. Typically the destinations tend to form two groups, one at each side of the map, and you can basically connect the cities on each coast and then done one railway across the country horizontally to finish all of the destinations. Once your train count drops to 2 or below, everyone takes a final turn and the match is over.
The achievement will unlock once the final scores are displayed. This can be unlocked in local play or on LIVE, but can only be earned on the 1910 Mega map. If you are playing on LIVE, every participant must have the DLC to join the match.