So in theory, this achievement is easy. All you need to do is input a target weight loss goal when you first start a weight loss program, and then you should unlock this achievement once you reach that weight loss goal during one of your weekly weigh ins.
However, the achievement (as well as the whole target weight loss system) is glitchy. A common problem seems to be that the game never asks you to input a target weight loss goal, and when you look at your weight loss stats following a weigh in, it shows your weight loss goal as "N/A". While some people have reported success starting fitness programs with different settings (initial weight, program length, etc.), I found that it didn't matter what settings I used in the initial fitness program setup, the game never asked me for a target weight loss goal, thus making reaching that goal impossible.
I was finally able to get it to unlock after completing the last weigh in during a 4 week program. During this weigh in, I told the game that I lost an impossibly large amount of weight in the last week (like 60 pounds), and in addition to winning The Biggest Loser achievement, this one randomly popped.
Good luck on getting your achievement to pop, hope my experience is of use to you!