Use 'slim down' when talking about personal weight loss as a goal or achievement. I managed to slim down for my high school reunion.
Pro Tip 2/3
Physical Transformation
'Slim down' often reflects a visible change and can be motivating when discussing physical fitness. After months at the gym, he slimmed down significantly.
Pro Tip 3/3
Not Overnight
'Slim down' implies gradual process, not an instant result. It takes time. I'm trying to slim down by summer through diet and exercise.