Furthermore, the Dwarfs do not need to be the ones controlling the settlement when you take it. You'll most likely want to stay friendly with the Dwarfs throughout your Empire campaign so I only recommend doing this after you have already won or making a save and reloading after you have earned the achievement. Playing as the Empire, raze the Dwarfs' capital at Karaz-a-Karak. The steam tank requires a high tier building to recruit so it may take you time, but it's not difficult to get to at all. Playing as the Empire, recruit a Steam Tank to one of your armies. Put 10 in the same army for the achievement. The Reiksguard will probably be your mainstay cavalry unit for a while in your campaign so getting 10 of them recruited won't be a problem. Playing as the Empire, have at least 10 Reiksguard units in a single army. This must be fought out on the battle map, not autoresolved.
This can be a combination of Lords and Heroes, it doesn't have to be three of one type. Playing as the Empire, win a campaign land battle with three or more Lords and Heroes in your army.