I got this achievement earlier this week. I can guarantee that you do NOT have to play consecutive days. I started several months ago and missed more than 10 days mixed in.
I can also confirm that you can get this acheivement by using the "time zone" glitch that I read about in another post here. Basically, you can log in with the TZ set to today. Get to the start screen and back out to the dashboard. Then, go to system settings and change the TZ to a different day. I'm in the midwest, so I would generally scroll down on the list of TZs until I crossed midnight to the next day. Then, head back to the start screen of BiA. After you get there, go
back to the screen to change TZ back to the previous day, and then back, once again, to BiA. Lather, rinse, repeat.
That means the game would count October 14 as day 1. October 15 as day 2. October 14 as day 3. October 15 as day 4, (ad nauseum.)
Every (real) day I logged was recorded on
my profile at 360voice.com. You can see that it only recorded 64 days, but I have the 100 day achievement. (I didn't really get into the TZ cheat until late in the game.)
I was skeptical, but I kept track of every day (and added hash marks for the days I cheated). I got the points on what I thought was day 98.
One shot, one kill. But I'm not worried; I'll respawn.