For getting this naturally, a month seems to be defined as 30 days.
I created my farm on 2/2, and although it doesn't tell you the exact time of creation, it was probably in the early evening for me, considering my schedule at the time. I logged in early on 3/4 -- the 30th day later -- and it didn't pop. But when I waited until after the time I would have started playing on 2/2, the achievement popped. So it seemed to be right at 30 days.
You can get the creation date of your farm by going to My Farms, then selecting the Details (Y) of your farm.