Hearthpwn

Overview:
Use removal to attack Romulo (so he loses buffs) and other minions, killing her with fatigue.

Mulligan:
Early removal: Slam, Warpath, Whirlwind + Execute and early taunts: Cornered Sentry, Stonehill Defender.

Early Game:
Use the removal and taunts to try and control the board as best as possible. Focusing on Romulo only if he is buffed or there is nothing else to do. She has a ton of taunts and draw and will do her best to keep him buffed.

Note: Keeping Romulo down is not a priority in the beginning, unless he is doing a lot of damage. Killing him will not allow him to attack the next turn. It's more important to kill him when he is buffed. He will also not attack a taunt minion if it will kill him.

Mid Game:
Continue to control the board and play the Drywhisker Armorer when she goes wide, save Brawls for these moments too.

Late Game:
She will get to fatigue quickly, but you may also near or be in early fatigue. Try to save removal and/or weapons for killing Romulo here (so Julianne takes damage). The Lich King should help with face if possible, while Saronite Chain Gang and Phantom Militia help with Romulo if you still have them. If you are using a Stonehill Defender here, try and find one that can take him out a few times, or can really help push face.

My Other One Night in Karazhan Decks:
The Parlor
     Silverware Golem (Patron Warrior)
     Magic Mirror (Silence Priest)
     Chess (White King)

The Opera
     Romulo & Julianne (Taunt Warrior)
     Big Bad Wolf (Resurrect Dragon Priest)
     The Crone (Murloc Shaman)

The Menagerie
     The Curator (Exodia Mage)
     Nightbane (Resurrect Priest)
     Terestian Illhoof (Thief Priest)

The Spire
     Shade of Aran (Aggro Mage)
     Netherspite (Freeze Mage)
     Free Medivh! - Prince Malchezzar (Jade Taunt Druid)