Valkyria Revolution

Battle Reports are essentially small quests that you can fulfill while on missions. They range from anything as simple as capturing a base, to getting kills with a specific elemental attack or weapon, to knocking tanks to their knees. You don't need to accept the tasks or anything - they're active right away and a new one will appear when you turn one in, but make sure you check what to aim for before each mission, and turn them in when you return if you succeeded with any. I wouldn't worry about trying for these during story missions so that you can focus on S-Ranks, but on Free and Battle missions, try and knock a few out each time.