So this is the bread and butter achievement out of the whole lot. You will need to watch 16.6 hours worth of material off of the app. By the time you finish all the other achievements you should be close to finishing off the requirement, but not quite there. You can take advantage of your achievement tracker to keep track of your progress.
Remember, there is no fast-forwarding trick to utilize with this app so you will need to either watch the shows, snap the app and do something else, or let it run on a playlist. Choose any show with an episode and let it play, repeat, and play until you hit the mark.