Just play one episode over and over while you're watching a movie or something.
1) load up the game
2) start an episode, any episode really
3) watch a movie, do some chores or whatever. The game should see you, though, at least once in a while, that's why I think watching a movie on your TV is best. You don't need to get a score in the episode or anything.
4) press A on the Xbox controller every five or ten minutes (whenever you remember you're actually playing a game) to start the episode again
5) the achievement will unlock when you've finished the tenth episode.
To break the streak, you need to quit the game, I believe... visiting the shop, the photo booth etc. does not (but this needs confirmation).