Pretty much what the description says really, simply play the game on every day of the week. This does not mean play it everyday in a row for a week straight, you just have to have loaded the game up on each day of the week at some point since you got the game. You will get this in time, but if you want it now then you can change the date on the vita system.
To change the date/day on your console, head for the "Settings" application on the LiveArea. Now follow the 'Date & Time' tab, touch the 'Date & Time Settings' button and then 'Set Manually'. Now set the date to one day ahead of today's date, then load up the game and play it for a bit and then do the same thing again for the next day. Repeat until you have completed all seven days. The trophy will unlock after the seventh day.