To get this achievement, efficiency is the name of the game. You need to get as many trains out of your supply per turn as possible; you start with 45 trains and four cards, and have to get your supply down to 2 to end things. Here's the listing of how efficient different routes are in trains out of your supply per turn.
Type of Route Ndd Turns Trains Usd Efficiency
1 Normal 1.5 turns 1 train .75 trains/turn
2 Normal 2 turns 2 trains 1 train/turn
3 Normal 2.5 turns 3 trains 1.2 trains/turn
4 Normal 3 turns 4 trains 1.3… trains/turn
1 with 1 X 1.5 turns 2 trains 1.3… trains per turn
5 Normal 3.5 turns 5 trains 1.428571…trains/turn
6 Normal 4 turns 6 trains 1.5 trains/turn
2 with 1 X 2 turns 3 trains 1.5 trains per turn
3 with 1 X 2.5 turns 4 trains 1.6 trains per turn
4 with 1 X 3 turns 5 trains 1.6… trains per turn.
2 with 2 Xs 2 turns 4 trains 2 trains per turn
So, whenever possible, choose routes closest to the bottom of the list, with some allowances for completing tickets and actually having the points for winning. Do not, however, waste a turn drawing more tickets. Good luck!