You don't actually have to watch the episodes for it to count towards this achievement. You can select or search for any episode under the "Entertainment" category... The easiest option to make sure it counts is to select one of the programmes on the first page. As soon as you select one of the episodes and click "Watch Now" it counts towards the achievement, so you can just press "B" to back out to the show's menu screen, then move back over to "Watch Now" and repeat this 10 times.
You can snap the achievement app so you can keep track of the achievement and make sure it's counting towards the achievement. If it isn't counting for you try using a different show. I used Russell Howard's Good News as it was on the home page, and it worked perfectly.