On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled The Bane. You can start this quest in the Sanctuary location after completing the main mission named The Once and Future Slab.
1) An Old ECHO Recorder
3) Passage north
Lynchwood- northern part
8) ECHO Recorder
Lynchwood - southern part
To the left from the entrance to Moxxi's place, you will see a dead NPC  from the above screenshot. Beside his body, you should find An Old ECHO Recorder. Pick it up, head to Marcus  and speak with him. Use Fast Travel and travel to The Dust.
Head north behind Ellie's garage . There you will find the corpse and ECHO Recorder of Horace. Head back to Ellie and use Catch -a- Ride. Go to McNally's house  and eliminate him. By his corpse you will find another ECHO Recorder.
Now head to the western end of the map. On the platform there will be a train, acting as a passage to Lynchwood. Afterwards follow the tunnel to the northern part of the area .
After getting out of the tunnel, on the left you should see the shack from the above screenshot , inside of which you have to destroy a fuse box. That way you will open a open a further passage to a chest .
At the end of the next tunnel you will find an elevator (screenshot)  which will take you to the upper part of town.
Clear the area and head to the building marked as . On the ground floor you will find the ECHO Recorder. On the same level of the town you will also find a chest in the trunk of a car .
Now head to the southern part of the area. In order to get above, use the elevator marked as number . Head south until you reach a grave  from the screenshot. Search it to end the mission.