Playing as England in Scramble for Africa, complete a railroad from Cairo to Capetown.
To get this achievement, you need to play the Scramble For Africa scenario.
To win this achievement, you must build a railroad from Capetown to Cairo. You must finish this before the game ends at 100 turns. The "Just one more turn" button is disabled. The railroad must connect through cities that you own or puppet. each railroad tile must be in your territory or in unclaimed land. If you just start at Capetown and go north, you will probably not have enough time. My strategy was send my lonely explorer north and check out the lay of the land, as it changes with each start. Then find two city states along the route and take them over with diplomatic marriage.
In the south, you will have to kill off the Boers, because their cities are going to block the shortest route. Before starting a war with them, get at least one settler past them and set up a new city in the jungle. As far as culture policies go, take the one with reduced road maintenance first and then work for the one with 3 free settlers. Start building your cities one after the other to meet your former city states in the north. Your costal towns will not be doing very much. Since you can not be attacked by the other european powers, you don't need to put a large number of units around them. Use these cities to build a huge naval fleet and send it to Cairo. This will take a while. 14-15 turns travel time. Send a couple of ironclads along with your frigates.
You will have to conquer Cairo and any other cities that Egypt has built along your route to win this achievement. Before attacking their first southern city, attack their costal cities in the north. This should cause the AI to send units to defend the desert cities. Much easier to kill them with artillery there than in the jungle. (You will need to buy all of your units and workers in the north once you have captured Suez or Alexandria. Gibraltar is pretty much useless for producing these units as it has almost no production resources. Sending the units from West Africa will be slow. But by then you will have lots of profitable trade routes, so there will be plenty of gold to spend in Egypt!) If you are lucky, Egypt will have built roads connecting all of their cities, so your purchased workers in the north can just follow your road of conquest improving roads to railroads.
There will be lots of barbarian attacks everywhere, so pay attention to your workers. You will not need to make many workers yourself, because the AI is very careless about sending their workers into the jungle unprotected, so just go around liberating barbarian camps and keep the workers. Don't worry about being on good terms with the Europeans. They are going to start denouncing you at about turn 50 anyway. You will have a continuous string of cities splitting the continent right down the middle. Watch out when they also get the social policy with 3 free settlers. There will be settlers everywhere looking for a home. Be sure their new cities don't cut your railroad off, or you will have to take it back from them by force. Best is to buy up all the tiles that your railroad is on. Also, unless you need passage, don't be too liberal with your open borders. Otherwise you will find your lovely railway clogged with workers and settlers from other european powers and be unable to move your fighting units from the production centres in South Africa to the north for the conquest of Egypt.
All in all a challenging achievement. You may be able to get a couple of other achievements done in the same game.