Select the Area 51 Challenge and start killing everything in sight. Wait for the big metal robot to appear from the right, but do not destroy it as it does not kill you. As soon as it enters the screen, stand directly under it and start shooting in the opposite direction. You will kill everything that appears from the left side and the enemies jumping over the robot with ease. Keep this up for about twenty minutes to easily unlock both achievements at the same time.
For the"Survivalist" achievement, enter the Urban challenge and get in any car. Stay far to the left and charge your gun. Whenever you see an FBI car, release your charged burst and the car will instantly die. Recharge the gun every time you kill an FBI car. Do not worry about the FBI agents on the top of the cars; they are clueless and simply jump around.