One of the marks of a good AU is that you can alter the personalities and/or environment of the story without it seeming too overdone. Rainbooms and Royalty succeeds at this.
The story premise starts with one change, Celestia is in Cloudsdale when the Sonic Rainboom occurs instead of in Canterlot. Thus, Rainbow Dash becomes her personal student instead of Twilight Sparkle. However, instead of simply turning Rainbow Dash into a Pegasus version of Twilight (in Rainbow Dash's own words an "egghead."), the author does a very good job at exploring just how Rainbow Dash would act were she living in Canterlot among the elite and in the Palace twenty-four seven. All the rules chafe her considerably and she doesn't make many (if any friends) due to all the people her age being to prissy and "uncool." However, the story goes into greater detail of the relationship between Celestia and Rainbow Dash (as it is in the story) which is honestly one of the best parts. Rainbow Dash is far more willing to treat Celestia as a person rather than a teacher than Twilight would be. Celestia in response treats Rainbow Dash more like a daughter than a student. Their relationship is very heartwarming.
The fanfic is essentially the first two episodes of the show according to the AU. That said, the fanfic takes far more time exploring the personalities and character of the 6 Bearers of the Elements of Harmony as well as a few other side characters. Two standouts are Ditzy Do (Derpy) and Shining Armor, both of which are given time and focus within the story. They are very well written, Ditzy functioning as a combination sister/mother figure to Rainbow Dash, and Shining Armor acting as the big brother/precocious crush for her as well.
The story as said before is essentially the first two episodes of the show. But, it doesn't simply follow the show and not deviate at all. It instead quite cleverly introduces many variations on the people and the tests that the Bearer's must face. The battles are given more time and thought to them, the characters develop and feel believable, and it even contains some clever shout-outs to various other fictional works.
This is a delightful story that fully embraces the fact that its an AU and uses it to its full advantage.
I give it a 9 out of 10. It is one of the better and more thought through of fanfics.