After completing Bright Lights, Flying City story mission, we can go and speak to Marshall Friedman, a new character from Sanctuary, to activate the Borderlands 2 Won't Get Fooled Again optional mission.
In Borderlands 2 Won't Get Fooled Again, Marshall Friedman wants us to solve the murder of Justin MacReady by questioning some key characters around Sanctuary, and identify the killer among the identical Gutter quadruplets.
"Marshall Friedman needs your help: one of the identical Gutter quadruplets murdered a boy in town, and Friedman doesn't know which one. You'll have to question the witnesses and use your deductive skills as you want to discover the true perpetrator.
Experience: 1305 XP
We can accuse one of the four Gutter brothers as soon as we begin Borderlands 2 Won't Get Fooled Again, but we don't know who to choose.
Therefore, we complete our secondary objectives, which require interrogating some witnesses around Sanctuary. The first one to question is Marshall Friedman, the one from whom we got this job. From what he's saying, he heard a single gunshot.
The next two characters that need to be interrogated are Moxxi and Zed. From Moxxi we learn that he's the one with a shield, and Zed tells us he patched up one of them.
So, the only one who fits the description (single shot weapon, shield, full health), is Barlo Gutter, the one with the sniper rifle. We accuse him just to be shot by Marshall Friedman, and then speak to Friedman to receive our reward and complete Won't Get Fooled Again.