Is it possible to loose 20lbs in a month?

I've been yo yo dieting for the last year, my weight has fluctuated from 228-140lbs then up to 170 down to 133 then up to 160 then down to 135 and it's now up to 140. I want to be 126lbs by july. If I REALLY commit myself and do everything I possibly can (Atkins, exercise , calorie shifting..) can I FINALLY get down to my goal weight. It is really frustrating me because I know I will look amazing if I was 9 stone. I'm 5'9 by the way.