You need to do this on the standard American map. The routes you need to claim are:
* Atlanta - Miami (Blue)
* Saint Louis - Pittsburgh (Green)
* Sault St. Marie - Montreal (Black)
* Helena - Omaha (Red)
* El Paso - Oklahoma City (Yellow)
* Phoenix - Denver (White)
* San Francisco - Salt Lake City (Orange or White)
* Portland - San Francisco (Pink or Green)
Generally, it's easier to do the last two with Orange and Pink, since then you're collecting eight colours. Besides that, you need to hope your opponent misses a ticket or two, because they will get longest route. You have five trains to play with to use for blocking or completing your own tickets. The following tickets are possible to claim and how many trains they use:
Denver - El Paso (3 trains) : 4 points
Kansas City - Houston (5 trains) : 5 points
New York - Atlanta (5 trains) : 6 points
Calgary - Salt Lake City (5 trains) : 7 points
Seattle - Los Angeles (4 trains) : 9 points
Toronto - Miami (5 trains) : 10 points
Portland - Phoenix (3 trains) : 11 points