Firing from the hip is done by shooting your weapon without aiming down the sights. If you are hiding behind cover and shoot it will count as "blind firing". This strategy does not work so well on the harder difficulties, but during your speed run you should get this. You wont have the time to be taking cover and aiming. Firing from the hip as you are running around is the easiest way to get the trophy.
Defeat 50 enemies from-the-hip or blind-firing