1up has some more information about what we’ve been seeing in the video updates.  They talk about how the multiplayer works and some of the other features in the game:

The battle mode is two-player over local Wi-Fi, and involves the competitive collection of variously sized Triforce pieces. Each player’s Link (red and blue) has their own designated strip of land (marked by color) which they must fill with as many of the Triforce pieces that are strewn across the map as possible.

Check out the video to see this in action!  Hopefully we’ll get some more info on the single player sometime soon.

Source: 1up