Start an Empire Mode game, and change the settings to no time limit and no edit officers (as they don’t count toward the achievement). Increase the officer limit to MAX, and turn off officer death. Now go through the story as normal till you have 1 area left you haven’t taken yet. Use the Long Treaty with them, and go to hire wide (you will need items to do this). All officers with GET! next to their name you have already gotten. Instead, continue down the list and hire everyone with a blank spot where GET! appears. Once you have found everyone you can (this can take multiple play throughs) save and beat the last opponent.
Keep playing through till you have all 250.