The best place I found to get this is during the fight club instances. You can unlock fight club by going to the Associates Activities icon on the map for Robert Topping. The icon should be on the upper left corner of the City of London section of the map.
As long as you are the same or higher level as the enemies you should be able to bring them down pretty easily. To perform a multi finisher you have to take at least two enemies health down to near death, they will be near death when their health bar is flashing and they will be stumbling around. Just get close to them to finish them off
Doing this you can pull off around 6-10 double kills during one activity. You can replay the same one over again until you get the achievement.