The pole swinging ability is required, so this achievement is Jake only. In Chapter 4 of Jake’s Campaign, after the motorcycle section, and after Chris/Piers help you defeat all enemies, you’ll enter an area with the grasshopper J’avo and your objective will change to shoot down the helicopter. Take down the J’avo and climb the ladders to the top of this area.
Wait patiently for the helicopter to come around to drop off some enemies. Stand near the rope and hit to grab on. Kill any enemies before doing this or they’ll be able to knock you off the rope. Once you reach the top, aim at the pilot and press for the kill and achievement. Once you've grabbed the rope, the whole sequence is basically a QTE which means you don't need to worry about having ammo or the right gun equipped.