The grandmaster's quests give faction also; there are two quests in game and two more coming soon (most likely next game update, barring acts of Bristlebane). Other than that, however, writs it is.
There is however an extremely easy way to get the mirror without doing any faction work: just ask someone who already has faction to make you one.
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(DominoDev) Re:AA Mirror recipe / faction required Question .....
