Quoted from markmon:Dies anyone know how to beat house targaryen? I start this and get a bunch of blue arrows to shoot for hurry ups. Then the dragon lights. I hit that to do some damage and other blue arrows light. Pretty soon it gets to a point where nothing is lit, the "drogon" has about half life, and it keeps flapping forever with no apparent way to progress or time out the mode.
Yes, I've beaten it. From the point you described, I think it was a final shot to the dragon, if I recall correctly.
I'm guessing you've already figured this out, but you have to play that house 3 times (to defeat each of the three dragons).