Instructions
Join a multi-player match. If possible, make a private match with just you and a couple of friends -- tell them you are trying to get the Lightweight Pro Emblem. This way you won't have to worry about fighting people and can concentrate on sprinting.
Join a match on a large map, such as Wasteland, Derail, Favela and Underpass. These maps will allow you to better find low-traffic areas where you can sprint back and forth without anybody coming to bother you.
Sprint for 30 miles. To sprint, you have to depress the left thumb stick while pushing forward with it. Once you hit the 30-mile mark, you automatically unlock the emblem.