Yay, achievements. Since I like to dissect anything concerning Persona 4 Arena, I wanted to post this and turn your attention to a few specific ones:
I have no clue what this could mean, actually. Obviously a reference to Persona 3 and Persona 4's battle music, which make appearances respectively in P3 and P4 mirror matches. Maybe it's awarded when you battle in your first mirror match?
Nothing special; this is just awarded in the game's Challenge Mode. Just posting it 'cause Funky Student's mentioned.
It's a bit ambiguous, but I believe this basically means you've completed all of the tests in the game's Lesson Mode meant for teaching players how to play the game.
Dunno. My guess is that this is probably more direct than it seems and it's simply rewarded when the Investigation Team tunes in to the Midnight Channel for the first time (again) early on in the game's Story Mode.
So everything else is pretty straightforward, except for the five Secret Achievements. There are already 10 achievements rewarded for completing all of the characters' Story Modes, but this is excluding Elizabeth, Labrys and Shadow Labrys. Given what happens in the story, I doubt S. Labrys will have her own story to go through, but I'm certain that Elizabeth will have one, especially because of a few seconds of footage from the MCM Expo recently that showed an anime cutscene featuring her. My bet is that Labrys also has a story mode after S. Labrys is defeated and she gains Ariadne, which means that 2/5 Secret Achievements are to complete Labrys and Elizabeth's Story chapters (two of the 10 pointers).
That leaves me with three others to guess. Because the person behind the events of the story (the one who threw Labrys into the television) has yet to be revealed, I'm guessing that one of the secret ones (one of the 10 pointers) is something like "The Investigation Team does it again" or "The True Criminal" which is awarded when the person behind everything is found out, making 3/5 of the Achievements. Given that this info will probably be discovered in the final Story Mode chapter and that, given how BlazBlue does it, there will be a final chapter not dedicated to any specific character, I'm guessing that another of the secret achievements is something like "The Final Story chapter has been told" (either a 10 pointer or the 40 pointer).
Which makes for only one left. Perhaps it's an Easter egg kind of achievement awarded for doing something hidden.