Avoid the cops at maximum threat level for 1 minute on foot, without taking damage
Start by reaching maximum threat level and drive to any area that has a good amount of walking space. Avoid narrow alleys and traffic on the streets. Circle around the building while swaying back and forth by jumping. This will make it hard for the police and Army to have a clear shot of you and just continue to chase you on foot. The Army carry Claws that will grab you if the Army gets to close to you.
Another method is during the mission Saved By the Bell, you will be told to beat up Squeak at the T-Shirt shop on the beach. Squeak will go down in one punch. Throwing punches will increase your threat level, keep punching Squeak even tho he is already down. The police and Army will not be able to touch or hit you since the area will be blocked by a fence.
You can follow this video by mjc0961. Described in the first method.