I did it on the US map, pass and play mode. Draw tickets for the horizontal route - Los Angeles to New York. Connect through the smaller middle route, don't waste cars on the long trip.
Once done, keep drawing tickets and keep the ones that fit into the network easily. You are looking for the San Francisco, Seattle, Portland, Boston, Montreal, Chicago ones. Avoid Miami, that would be too much of a detour. If you open ones you cant complete within the network, draw the smallest value so you won't suffer too much penalty.
Keep tracking the score you will earn from the tickets, as you cant see all completed ones in the game. Once above 300 including the 25 from long route and globetrotter, finish the game.