Nightmare Moon doesnt exist quite as such in the Diplomat-verse. Instead, its mostly a nickname given to Luna by criminals who fear her effectiveness as Celestias enforcer. However, there is an incident which historians informally refer to by the same name.  
At the time, Luna was beginning to ignore all authority save Celestias personal word in her pursuit of criminals, even going so far as to ignore established laws and citizen rights. Nightly raids and brutal interrogations were no rarity and even a few on-the-spot executions were said to have occurred. In short, even the law abiding citizens came to fear her. Celestia would do nothing to rein her in however. Too strong were her sisterly feelings and the results of Lunas tactics.  
Finally some court attendees and members of criminal organisations decided to get rid of Luna by setting her up and framing her for attempted murder of the empress. Celestia was forced to banish her own sister.  
In exile, Luna re-found her inner balance and sense of morality and when she returned, she hunted down those who had framed her and brought them to justice. Celestias justice, in open court, this time.