YouTuber pm00 really does make the best video guides for The Elder Scrolls V: Skyrim. In order to get the 'War Hero' achievement, you'll have to complete a few objectives. First and foremost, you'll have to join the Imperial Legion to activate that questline. Also, you'll have to complete the quest "Compelling Tribute".
Now, to get the 'War Hero' achievement, you'll have to capture Fort Sunguard or Fort Greenwall for the Imperial Legion. Do this, and you'll get 10G on Xbox 360, or a bronze trophy on PlayStation 3.