Awesome action, awesome game.....but the plot does need a bit of work. Oh, and it's short. Full review - and spoilers for the game - inside!
I'm not an excellent reviewer, so this is by no means a professional review - so it could be considered as my impressions. Unfortunately the PS Vita does not allow screencaps of PSP games, so I can't show any here, aside from the one used above, since I ripped the OP movie from the game and used VLC to screencap it. But let's get right to it, shall we?
You don't need to watch the OVA or anime series to understand just what the hell is going on in the game. And even if you do, there's ZERO plot connection between the game and anime series/OVA. The only thing that's the same is Black Rock Shooter herself. That's it.
An alien race has - for whatever reason (more on that issue in the spoilery section) - decided to invade Earth and take over it. 14 years have passed, and the humans have always prepared for a counterattack but never actually happened. Now, only about 10 humans remain before humans are extinct. So what do they do?
They have a secret weapon with them - and that is, the Black Rock Shooter, abbreviated as BRS. A girl that's cute as fuck, but won't hesitate to destroy her enemies. Especially her rival, who greatly reminds me of...
.....Yeeeeeaahh. (Hmm, I wonder, in Hyperdimension Neptunia Victory, if Anonydeath ever looked at Black Heart's ass the way I am now? Hmhmhmhm.....OW!!)
I'll talk more about the story later and give examples of some of the plot holes, in the spoilery section.
EDIT: There is a second ending. To get it, first you have to beat the game normally. After that...well, let's just say some of the missions have "mysteries" behind them.
This is a JRPG at its core....but I consider it to be an Action JRPG. Because when you encounter enemies on the field, you basically fight on an on-rails shooter.  to shoot, X to guard, and O to dodge. You aim with the D-pad, and shoot (about 5 bullets or so) at the enemy. But shooting and dodging - which, by the way, can mean life or death in some situations, especially during endgame boss battles - builds up heat, and when your Heat gauge gets full, well, you're a sitting duck (unless you use a certain item with L). Oh, and you can pull off your badass moves (and the animations that come with them) with R + face buttons.
Outside of battle, though, you're on a mission. Each Stage (of which there are only 6, and spans worldwide locations like New York City and Tokyo) is divided into 5 or so missions. Most of the time, these missions will have you killing specific targets or getting to a particular destination. During the last story mission (of each stage), though, you face off with that stage's boss. And you better come prepared - remember Final Fantasy XIII, where the only way to get Gil was to kill enemies? Well, the same thing applies here - but for items. 'Cause you're going to need them!
I don't care that it's a PSP game being played on my PS Vita. The graphics are awesome! But of course, there's the jaggies and such that really doesn't bother me.
Audio-wise, yes, the game is subtitled - meaning, Japanese audio only. I thought it was pretty good too. I also kinda liked some of the BGM, and ESPECIALLY...the opening theme song, No Scared, by ONE OK ROCK. I listen to that and the other 2 songs on their album, and as I imagine me and and BSR fighting together while I'm walking around outside, it goes quite nicely with her. Hopefully that makes sense to you guys.
And the cutscenes - which you unlock by completing each Stage's Free Hunt mission, which means you have to beat the boss again - are well-done, too, except if you view them from the Gallery, you view pre-rendered versions of them, which make up about 700MB of the game's size. The opening was just as badass as her and the song!
I'm going to close this out now, and say that if you have $20, 1GB, and like anime, go for it! I'm not going to give a score, because quite frankly I'm bad at doing that.
Now if you'll excuse me, I'm going to go watch the anime series and OVA....
...But you wanna know what's wrong with the story, right? Well, I suggest you stop reading now, as you are entering the...
NOTE: I haven't activated all the Yellow Terminals yet, not sure if that unlocks additional endings or not. Don't actually tell me what it does, though!
This is where I talk about the story itself. So when you first start the game, you fight White Rock Shooter as your tutorial battle. After that, she winds up in the trailer with the humans. How she got there is beyond me, and the game doesn't bother to explain it. Not to mention, she forgot everything!!!
Later on in the game, just as she starts to understand the human survivors (and even became friends with one!), they were attacked (again, how? I mean, I know who did it, but still...), and now she's the sole survivor (kinda like the Dominion gametype in Halo 4 where the enemy team has all the bases and all of your teammates are dead, spectating you.). Then there's a mission that's literally called "..." where she feels depressed (even on the Stage Select screen), and doesn't know what to do now. Then there's this whole "Nana working with the enemy" thing that doesn't make sense... Oh, and Black Rock Shooter isn't even her real name.
And there is a cliffhanger. Right before the game's credits, she literally says "I'm not a White. I am a..." and she never finishes it. Maybe she intended to say "Black Rock Shooter.".