The first two words Samantha Shane (played by Brooklyn Decker) says to Alex Hopper (played by Taylor Kitsch) are "I'm hungry." By that right, the film could have just as easily been called "Hungry Hungry Hippos", because that gives it about as much similarity to that game as it has to the other Hasbro board game for which it is actually named.
We quickly learn that Alex is a complete screw-up. His brother Stone (Alexander Skarsgård) is a commander in the Navy who has come to regret forcing his brother to enlist because he creates a lot of headaches. His latest infraction, a skirmish with a Japanese sailor during a soccer game, will likely net him a dishonorable discharge (from Liam Neeson's character Admiral Shane, the father of Alex's girlfriend Samantha), but before that happens, he's to participate in a set of international war games off the coast of Hawaii. And despite his detestable personality and utter incompetence, he somehow managed to get command of one of the ships.
But the war games are interrupted when actual war breaks out. But this isn't war with another country or independent rebels, but with aliens who come from a planet very similar to Earth and are now intent on taking over our planet as well. They've come in vehicles that work equally well in space, in the air, and in the water, and are armed with some pretty advanced weapons and defenses. One of the ships is able to serve as a kind of force field generator, and while its force field is able to keep out most of the world's armed forces, it just so happens that the ships piloted by Alex and his Japanese soccer rival are inside it and may be humanity's only hope.
Battleship is basically a naval version of Independence Day, complete with a Jeff Goldblum equivalent communications nerd in the form of Hamish Linklater, a Vivica A. Fox equivalent in the form of Rihanna, impenetrable energy fields, and a black man punching an alien in the face. But they also "borrowed" liberally from other sources, like giving the aliens a stupid and implausible weakness a la Signs and getting assistance from a bunch of over-the-hill veterans like Space Cowboys. They took the appearance of the alien suits from Halo, and the appearance of the aliens inside the suits from humans. They even managed to rip off Matt Damon's face and put it on the body of Jesse Plemons.
About the only source material that appears to be largely safe from plagiarism is Battleship the board game. I know that the artillery fired by the alien ships is supposed to resemble the pegs players stick into the game board, but unless the filmmakers had a different version of the game than the one I played as a kid, they didn't go out of their way to make them too similar. And only a couple of the movie's 131 minutes involve targeting alien ships with grid coordinates, but even then they chose to obscure the reference by using words like "bravo" and "echo" instead of letters like "B" and "E". And of course the one phrase that comes to everyone's mind when thinking of the game is nowhere to be heard.
At no point does anything in Battleship approach the vicinity of a good movie. It's possible that it could be fun with an audience that enjoys watching bad movies, but it's completely out of place in its attempted position as one of the summer's flagship films.