Begin by speaking to Madeleine at the inn in Cassardis after defeating the Hydra at the beginning of the game. She will ask you to escort her to the encampment. Do so without her dying and she will ask for 1,000 gold to start her own business. Give her the 1,000 gold.
Once you've reached Gran Soren, complete the quest "A Matter of Myrmidons". Now you should be able to find a man named Mason in the Fountain Square sometime during the day. This is the man who spoke to you when you first entered Gran Soren. If you don't find him in the Fountain Square, complete a couple quests while you wait or try sleeping at the inn.
When you do find him, you can start the quest "Chasing Shadows". Stay at the inn until nightfall, then make your way up the hill to the Noble Quarters. Now follow the knight to the abandoned house. Speak with Arsmith to complete "Chasing Shadows". Try sleeping or exiting then re-entering Gran Soren so her shop is no longer called "Abandoned House". Now speak to her and the achievement will unlock.
Some people have mentioned they got the achievement without escorting Madeleine. That didn't work for me and you will need to escort her for The Hero achievement anyway, but you can try speaking to her if you missed the escort quest and completed "Chasing Shadows".