I absolutely loved Vivid Strike. After watching it twice and thoroughly enjoying the action and drama both times, I've come to the conclusion that it's one of, if not the most underrated anime on MAL (in my opinion). With that said, the specials were a nice, fairly enjoyable way to get a little more out of the show and spend a bit more time with the characters but they don't really add anything of value to the story. The first two episodes take place between episodes 5 and 6 of the original show and mostly contain parts of the story that apparently weren't important enough
to be included in the main series. The first special does have some good action as Fuuka fights two girls in "mixed magical battles" instead of just martial arts. That's the only time you'll get to see some more fights in the special.
The final special episode is a 24 minute beach episode. If you were hoping to see Fuuka and Einhart's fight (I was), you won't, you'll just get a brief summary in the beginning about where all the girls' careers in martial arts and magical battles are going and then... a beach episode, a pretty average one at that. I mean, I'm glad to see Fuuka and Rinne together some more, but I didn't get a whole lot out of the episode beyond that. Seems pretty anticlimactic to hype up a big fight at the end of episode 12, then make a special episode numbered 13 and completely gloss over it with a brief summary that doesn't even explicitly say who won (heavily implies who wins though).
Art and sound are fine, good as the original series which I think looked pretty great and had a good opening theme (only plays in the 3rd episode of the special). Not much else to say here.
I didn't enjoy this as much as the original series, but I enjoyed it for the purpose of completing the series and at least getting to see a little more of Fuuka and Rinne whom I'll probably never see anywhere else again since this show wasn't that popular. Recommended for those who really loved Vivid Strike like I did, but if you didn't like it these specials won't change your mind. I was a tad disappointed but I don't regret watching.