Girl to Bring Home is one of 5 (non-result based) achievements you can get during your second Matchmaker interview. It’s for getting really high approval with the various factions. 
Ways to incur approval from external factions include mainly succeeding at public challenges, like the introduction speech and the boat race, as well as throwing successful events. Merchant approval can be raised by any opportunity to spend money. Rebel approval can be raised by invoking Katyia's legacy or being kind to servants. The second question in the Character Creator determines initial approval from one faction that is not your country of origin.
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