You must play in Offline Mode for over 5 hours in order for this to unlock. Whenever you are playing in any Offline Mode such as Arcade, Versus, Training, or Mission this will accumulate. Leaving the game on idle under Training or Mission Mode should help you work toward this, however you should easily net over 5 hours while working towards other achievements.
You can check your time progress for this achievement by checking your Battle Records from your License at the main menu by hitting . Hit again to see your Battle Records located at the bottom left of your screen.