I have those tips:
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.)
http://www.youtube.com/watch?feature=player_embedded&v=pVmoJXKjVdc&t=2
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Just continue and make a peace treaty (Main Quest) between the Legion and the Stormcloaks.
- If you side with the Stormcloaks then Markarth must remain an Imperial city and you will be guided to take Fort Sungard fairly early on. After capturing the fort the achievement will pop.
- If you side with the Imperials then Riften must remain a Stormcloak city and you will be told to capture Fort Greenway.
Upon completing the main quest the two dominant factions will reignite the war once again allowing you to gain your achievements.
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To join the Legion travel to Solitude and enter Castle Dour and speak to General Tullis.
To join the Stormcloaks travel to Windhelm and enter the Palace of the Kings and speak to Ulfric Stormcloak.
This achievement is for playing halfway through either side's story-line and capture a fortress. Which is either Fort Sungard or Fort Greenwall depending on who you side with.