Dynasty Warriors 7

To get the wallpaper for each character, you need to complete their legendary battles in Conquest mode and make them a sworn ally in Conquest mode. To make them a sworn ally, you need to get their bond up to about 20%, which can be done by calling for them as reinforcements, saving or defending them in missions. Once the bond is high enough, they will appear in a town (assuming you have completed at least one of their legendary battles) and you can talk with them to make them a sworn ally.

To get the faction-specific wallpapers, you just need to beat Story mode as that faction.