Chris arose from the dead with this:

(This makes me unconvinced that Akane actually is as terrible a shot as she seems to be. It doesn't even have to be deliberate and conscious on her part. Really, humans are startlingly kind when you get down to it; outside of cliched shounen action series, you usually have to work quite hard to get them to hurt and kill each other.)

As for Akane: I think she's just manic (okay, very enthusiastic). Shizuku is just an excuse to let off some energy, as Natsuru was at the start of the show.

I thought about this, but it doesn't seem to be the case. Sparring this way only works if both sides refrain from escalation, and that is only possible with an ahead of time agreement. We don't know if Akane fought with Shizuku before; consistency says that she didn't (because both of the "partners" were hardly a match for the Prez later; alone she would be a dead meat). So, she's facing an enemy of unknown powers. It is not credible to think that she would hold back when her life was at stake.

Suppose that Akane thinks that she's invulnerable, so it all is a play for her plausibly. In that case, isn't she sadistic?

In the end, I think she really did miss, thanks to various circumstances and how Kampfers seem to be balanced towards defense. Shizuku missed no less. Authors set the fighting this way in order to prevent characters being killed off too soon.

UPDATE: We have new evidence that Akane is a poor shot and misses on purpose as well. Chris comments further.