Boggs has just had both legs destroyed in a bomb. He's dying, and in a terrible way. Yet he still clings to life to accomplish one final task as a soldier and serve his cause by giving control of the Holo to Katniss. If he doesn't do so, it will be unusable. The fact that Boggs can put aside the incredible pain and terror of dying to focus on his duty shows just how courageous he is.