You need to kill a FIB agent at the Merryweather Headquarters and then escape.
Walkthrough of the First Martin’s Dispatch Mission
Head to the police station and start shooting cops. When all the enemies are eliminated, go through the door to the right of the entrance and then down the stairway. There you need to eliminate two cops in the cell room.
Now you need to open the door using explosives or the computer that located in the room. In the second case, the controls of the character become a bit strange. Don’t pay attention to this and press the action button until the door open.
Go to the last cell of the corridor and assassinate the target. After that, you need to go back upstairs where police and NOOSE will attack you.
You can leave by the same way that you arrived, or through the roof. In the first case, you will be involved in a massive shootout. In the second case, you will need only to defend yourselves from attackers inside of the building, which is easier.
If you have chosen the second option, go to the roof through the door with a sign saying “Locker Rooms”. Get in a helicopter and fly away from the police station. Try to gain altitude as soon as possible in purpose that policemen on the ground won’t be able to see you. Also, avoid police helicopters. When you lose the wanted level, the mission will be completed.
Video walkthrough: youtu.be/POHbGu3KExA.
The mission accomplished on hard difficulty by two players. Thanks to Eugene for help.