This challenge, part of the "Forged in Slurp" mission is to perform eliminations, but at specific locations on the map. And if Retail Row is one of the most famous places on Apollo Island (it is even one of the few surviving places on the S10), it is not the same for the E.G.O. outposts. These notable places are scattered over several places on the map, and all look like small militarized strongholds.
Map
Two methods are available to complete the challenge quickly. The first is to land at Retail Row, especially the week after the mission's release. You can be sure that many players will rush to the site hoping to finish their challenge, just like you. The second one is to play in Team Rumble to favor the E.G.O. outposts to find and kill opponents.