Here's how to find out (or see Shog9's answer if you use Greasemonkey). Go to your profile reputation page (the one with the chart on it), View Source, and find the line that looks like this:
var d = [[1238832000000, 10],[1240300800000, 20], ...
Paste that, without the
var, into the top of this Python script:
d = [[1238832000000, 10],[1240300800000, 20], ... qualifying_days = 0 previous_rep = 0 for _, rep in d: if rep - previous_rep >= 200: qualifying_days += 1 previous_rep = rep print qualifying_days
That will print the number of days you hit 200 points. (That probably isn't an exact match for how the badges are calculated, but it should be ballpark correct.)