Boulder City Showdown appears when you reach Boulder City when trying to intercept the Great Khans during They Went That-A-Way.
When you speak with Lt. Monroe at the entrance, he will mention that there are two hostages within the boulder city ruins. As with most Fallout quests, there is more than one means to complete the quest.
Stealth and combat[edit]
If you choose the stealth option, the Khans will be hostile. The easiest method to rescue the troops is to sneak around the far left hand side, and pick the back door lock. The two NCR soldiers can be brought out from the back door, and will return to the entrance to the ruins.
Once they are rescued (or if you get detected), you will need to eliminate all remaining Khan troops. The captives will not be harmed, and the NCR troopers are more than able to defeat the remaining Khans.
Negotiation[edit]
With sufficient speech skill, you can convince the Khans to leave peacefully, by speaking with Jessup in the back room. With this option, you will gain slight fame for the Khans.
Khan Escape[edit]
Eliminate all NCR troops within and outside the ruins. As with the negotiation option, you will receive the cigarette lighter.