To get the Bard stronghold, choose Bard as the class for your main character. Go to the Bridge district in Athkatla and speak with Raelis Shai inside the Five Flagons Inn theatre/basement. She'll give you the quest "Free Haer'Dalis from Imprisonment by Mekrath". Complete the quest, taking both Haer'Dalis(as a companion or otherwise) and the gem with you, and meet back up at the theatre. Accept to defend the troupe while they're opening the portal, which will give you the "Rescue Raelis and Haer'Dalis from the planar prison" quest. After the troupe has been captured, follow into the portal, and finish the quest. Receive the deed to the theatre, and the achievement will unlock.
Note: This can be done immediately after the prologue and speaking with Gaelan Bayle.