**AS OF NOW THIS ACHIEVEMENT IS UNOBTAINABLE, WILL UPDATE WHEN THE NETFLIX ACHIEVEMENTS ARE WORKING AGAIN. **
I have found this achievement to be very buggy. if you want to get this I have found that its best to load Netflix up and then compare games with a friend and look at more info to make sure it added another day. I have had this achievement reset on me like 3 times at 10 days each.
YOU DONT HAVE TO WATCH ANYTHING. JUST OPENING THE APP AT THE CORRECT TIME WILL WORK.
Edit: The reset time for netflix is the initial time you watched on the very first day, so if you started on the first day say 3 O'Clock pm, that means each day resets every day at 3 pm. It is also believed, although I'm leaning more to what I said above, that the days change on Netflix @ 4pm PST which is actually 12am GMT. (thank you Shinwasha)
The Video Below shows you how to check the consecutive days watched.
This is a video I made
YOU HAVE TO COMPARE GAMES WITH A FRIEND THAT HAS USED NETFLIX