Let’s keep it simple. Battleship is only good when there are ships and there is a battle. So skip to just before the combat begins, anything that happened in the first 30-40 minutes or so you can work out for yourself by the end, and the battle sequences are a lot of fun to watch. If you try to sit through the set up you’ll never make it to the good part. And it was good. Almost as if it were a different movie.
When you see the objects hurtling toward the earth’s atmosphere, that is probably the best place to start.
If you’ve got premium channels, by the way, the movie is currently available there as well (HBO I think), and worth the DVR space, assuming you skip the beginning.
So do you want spoilers?