Superman/Batman: Apocalypse (PG-13)
DC Comics; IMDb; TV Tropes; Warner Bros.; Wikipedia; World's Finest
Caution: potential spoilers.
This is, according to the internet, a sequel to Superman/Batman: Public Enemies, though I didn't realize that while I was watching it. I should also say both movies were based on comics I haven't read. And... I don't think it's at all important to have seen the previous movie before watching this one. I had, but it really did nothing to enhance my understanding or appreciation of events in this movie. There were perhaps a couple of references to aspects of Public Enemies, but they were things that just as easily could have been accepted as originating in this movie, I thought. (I mean, especially if you're a fan of Superman stories in general, and have a fair knowledge of things from various incarnations.)
Anyway, something crashes into Gotham Harbor, and Batman goes to investigate. Before he gets to what turns out to be a spaceship, someone has already left the scene. It turns out to be a naked girl who only speaks some alien language. Batman soon tracks her down, after she's caused quite a bit of unintential damage (due to her inability to control her super powers), and subdues her with kryptonite. She later awakes in the Batcave, and nearly escapes, but is stopped by Superman, who understands her language. It turns out the girl is Kara Zor-El, his cousin. He wants to look after her and help her learn to control her powers, though Batman is wary. Eventually, she goes to Themyscira to train with Wonder Woman and her fellow Amazons. There she befriends an Amazon named Lyla (aka Harbinger), who's had prophetic visions of Kara dying. (Though Lyla and Kara both look quite similar, and we never see the face of the girl who died, so it's easy to speculate that it might be Lyla. It's unclear why none of the characters made this speculation. Also, in the vision I don't really think it's entirely clear that the body is really dead, so regardless of which character it turns out to be, I'm not sure why everyone just seemed to assume not only that it was definitely Kara, but that she was definitely dead. Anyway, I am not going to reveal the truth about either supposition.)
Meanwhile, on the planet Apokolips, Granny Goodness is overseeing try-outs for a new warrior to become captain of the guard for the Female Furies, since Big Barda had defected. When Darkseid discovered that Kara had landed on Earth, he wanted the Furies to bring her to Apokolips so he could turn her to his side, to lead the Furies. When she's abducted, Superman, Batman, Wonder Woman, and Barda team up and head to Apokolips to rescue her.
And that's all I want to say about the plot. But there are a lot of awesome battles, and some humor. And basically it's just a pretty decent story. As usual, Batman is the best superhero ever. And Kara was pretty damned amazing, herself.
The DVD also includes a DC Showcase short film, Green Arrow.