On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Hungry Like the Skag. You can begin completing this quest during your first visit to the Arid Nexus Badlands location. This happens right after you complete the storyline mission named Data Mining.
Arid Nexus Badlands
1) ECHO Recorder
2) Skag caves
3) Bounty Board
As you fight with Skags, there's a chance that one of the enemies will drop an ECHO Recorder. In my case, I found it around the area marked as .
Listen to the recording and start killing Skags around  on the map. Random Skags might drop parts of the weapon after being killed. If you kill all the Skags in the area and still miss some parts, leave the location (Fast Travel, passages) and return to respawn the enemies. After collecting all the parts, head to the Board  to collect the prize.