The Hunter order in Modern Warfare 4 DMZ requires you to find a Lieutenant Hunt Tower and use its terminal to locate the nearest lieutenant. It is an easy order to accomplish since you do not have to fight the lieutenant. All you need to do is locate the tower and operate the terminal.
PG 2 Hunter Challenge Guide

In order to accomplish the Hunter mission, you have to find and climb a Lieutenant Hunt Tower and use a terminal on the top of the tower to search for a lieutenant. Lieutenant Hunt Towers are highlighted in yellow on the map if you zoom out. When you get closer to those, they will become white on your map to make them easier to spot. Go to the nearest tower and climb up to the top to use the terminal.

Please note that these towers are not the places where lieutenants are located. Rather, they help to obtain the coordinates where a lieutenant can be found. After using the terminal, a lieutenant will be highlighted on your map. Climb to the top of the tower and use the terminal there. It will scan the area for a lieutenant and highlight it on the map. After marking the coordinates of the lieutenant, the mission will be accomplished. There is no need to pursue or kill the lieutenant after the location is found.
Lieutenants are often hard to spot due to the fact that they normally hide in dangerous places rather than being in plain sight. Spot the marked area and get ready for a battle before going there. Once you have used the tower’s terminal to locate a lieutenant, you will have completed the main objective of the Hunter challenge.
