This achievement is for doing a side mission called "Don't Shoot the Messenger".
To activate this mission, you need to find a mysterious ECHO device as you make your way through "Tycho's Ribs" during the final story mission "The Beginning of the End". The ECHO device (appears as a exclamation mark on map) is lying next to the giant cannon that you have to commandeer to disable the giant force-field, allowing you to proceed further in the story.
Once the mission is activated, you will travel to "Triton Flats" and complete 3 objectives: Find messenger, Kill scouts (~5 or so normal enemies), and Talk to Hanna.
After talking to Hanna, you simply need to travel to "Concordia" to complete the 4th and final objective: Deliver note (to a person named Brittania in Moxxi's bar).
This mission should only take you ~10 minutes in total.