On the far wall (to the left when facing the big Mr. Head through the door to the left and jump over the railing. Keep using the pistol if you haven't reached 15 yet as there are a few other bots on this floor after those first 2 if you need them. At this point switch to your strongest weapon to take out any other robots in your way as the pistol sucks even on Very Easy. Kill Jane and the nearby Securitron and you're done with all 15.
Kill Victor (yes, Victor again) and the 2 robots with him to reach 13/15. Proceed to kill all Securitron MkII's in sight and Victor by the Lucky 38's entrance. On your way out, use VATS mode to blow the Right Arm of 5 of the Kings members. Inside, head upstairs to the second floor and grab the 9 Iron off the floor in the room right in front of you. Head down the street to King's School of Impersonation. Now warp to The Strip North Gate and kill all the nearby Securitron Gatekeeper robots with the pistol (should be 5). Warp to Gun Runners outside Freeside and purchase a 5.56mm pistol (the GRA version is best if available) and a Shotgun (the Riot Shotgun is best if available). Bring any 5.56mm, 12ga, and 12gaammo you have with you.
Load your Base Save from the main game that we set up before doing faction stuff. House with a 9 Iron or Nephi's Golf Driver) Benefit Or A Hazard (Kill 15 Robots with a 5.56mm Pistol) Ne Ne Ne Ne (Disable 5 Right Arms with a Shotgun)