Chapter 2 - Section "You have the Intel?"
The best place to get zipline kills is the second chapter. You can start working on this as soon as the "You have the Intel?" section starts. Select the zipline ability for the OWL and press L1 to use it. You must be standing at an elevated positon to use the zipline. Just keep firing at enemies while using the zipline until you have 5 kills in total. You could easily do 15 zipline kills in this chapter. Just let the enemies activate the alarm, go to an elevated position, kill the reinforcements using the zipline and repeat. Many enemies are just standing around at one spot, so they are easy targets.
You don't have to do this in one run. You can do 3 kills on your first playthrough, then do the remaining 2 the next time. However, restarting the checkpoint or section will reset your kills, so farming this via restarting the checkpoint will not work.