In Borderlands 2 Showdown given the events from the previous missions, the Sheriff wants a one on one confrontation with us, in a classical western style, pistols only, at noon.
Its time to take down the Sheriff.
Item: Eridium Artifact
Experience: 5716 XP
First we have to take a left once we exit the train station and travel to the settlement from the north side of Lynchwood area. This time, however, the place is deserted, with the exception of the Sheriffs station. Once we get inside the area waypoint, she will send her men to attack us.
A secondary objective in Borderlands 2 Showdown is to kill her with a pistol while not shooting her Deputy (an obvious reference to the popular song I Shot The Sheriff performed by Bob Marley).
Therefore, we take care of the Marshalls first, and then we concentrate our fire on the Marshall who is on top of the station. Sooner or later she will get down, making our job easier.
We can shoot her with any weapon we want, but its important to give her the final blow with a pistol to complete the secondary objective.
After shes done, the mission can be turned in, so now we can kill the Deputy too.
We should also note the fact that the residents will now come out from their houses to attack us, meaning we either kill them, or we either run.
To complete Borderlands 2 Showdown we turn it in at the bounty board inside the train station.