You must play in Offline Mode for over 30 hours in order for this to unlock. So 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 not bother leaving your console on idle for this until you have most of the offline-related achievements in the game, especially Master of Tasks. There's a fair chance you could be quite close to the 30 hour mark once you have completed 480 missions in Mission Mode and all other offline 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.