For this achievement you must follow all threads (Story Modes) to their inevitable conclusions. So in other words, you must complete Story Mode with all 8 characters. To access Story Mode go to Single Player from the main menu. Story Mode is quite short, including only 6 fights for most characters. The 5th fight is usually a 1 vs 2 fight followed by a final boss fight against Bloody Marie, the unplayable final boss of the game. Be warned, this game can have some pretty difficult A.I. So to make this easier be sure while you're in the Single Player menu, to highlight the difficulty and switch it to Sleepwalk. Also you may want to go to Help & Options from the Main Menu then Settings. Switch the time to 30 seconds to make things faster. Your options should be like so:
Time: 30 seconds
From the start of the game only 6 Story Modes will be available. Valentine's and Double Story will be locked. To unlock them, complete story mode with all 6 available to unlock Valentine's Story. Complete Valentine's to unlock Double's. Once you have completed Double's Story Mode this will unlock. The story is actually pretty decent in this game but you can skip cutscenes and dialogue by hitting to speed things up.