Just wanted to clarify 2 things:
1) You do NOT need to own the No Step Back DLC for this achievement to pop.
2) The railroad CAN go through territory owned by Neutral and Enemy countries. It CAN also use railway owned by Neutral and Enemy countries.
My railroad went Gibraltar to Madrid, Paris, Berlin, Moscow. From there I followed the Trans Siberian Railway until the North of India where I connected to Delhi, than through Bangladesh and Finally connecting at Rangoon which connected me through Siam and into Singapore.
EDIT: I did own Gibraltar and Singapore, not sure if thats a requirement or not.