Encounter: Drawbridge (Chapter 10)
Select the Drawbridge encounter from the main menu (chapter 10). Make sure you put it on Explorer difficulty and disable auto aim in the control options. There are two ropes in this encounter. The one on the right side works best. Use the rope and wait until it stops swinging. Then shoot the enemies in the head. The AK-47 (or any other assault rifle) work really well for this. You can fire in bursts and should easily get a headshot. The enemies aren't far away. Some will be standing right in front of you on a building. After killing a bunch of them restart the encounter.
Do not complete the encounter! Leave one alive and restart checkpoint! Each time you load up an encounter your kill counter resets. This means you must do 20 rope headshots in a row via checkpoint restart. If you quit out to the main menu your progress will be lost.
This should only take ~5 checkpoint restarts as you can get multiple headshots on each run.