The Black Eye skull is a gold skull. It is the first skull on the second level, Crow's Nest, and is in the same room you start in after the cinematic, high above your head atop a large pipe.

Getting to it is relatively easy. Walk to the end of the room, up a short staircase, and turn around and look for a green shelf. Jump up on that, up onto a girder, and from there up onto the large pipe. Walk back the length of the room to the end of the pipe nearest the video screens and claim this skull.

Black Eye offers an achievement and 150% bonus on campaign scoring. In return, your shields will not recharge as usual; you need to melee attack enemies to recharge your shields.