Perfectly Peaceful

Perfectly Peaceful

This is available at Chapter 11: Wildlife Preservation. Talk to Sir Hammerlock to start this mission. This is best done alongside with Marcus' Safe and Sound mission since they're both located in the Caustic Cavern. To reach it, you have to return to the hole where Sanctuary is once located then use the lifts down to reach the entrance of the cavern.

Once inside the cavern, you can find the first echo recorder on the trash pile near the dump trucks near the entrance. You can kill crystalisks and some varkids along the way as well. Continue forth and avoid the corrosive fluid all around you. Make your way to the Rumbling Shore where several threshers await. Kill five of them as part of the bonus objectives. Be careful not to get caught between them as they can easily rip through your shields.

The evidences are marked in the map so you just have to go to their general locations and find them. Make your way to the Infested Warehouse and find the second evidence on a foundation. Exit the warehouse and make your way to the Abandoned Mining Site. Examine the old Echo on the post to get a new optional mission.More threshers will appear here, including a Badass Pyre Thesher. Keep distance and destroy it and move on to the next location. 

Next, you'll find another recorder in the northern peak of the area, attached to a tombstone. The last one is located inside the Deep Core base in the southern portion of the map. I recommend doing the Minecart Mischief quest after getting the third recorder as that mission will lead you to the crusher. Just jump down to the lower level and you'll reach the room where the last recorder is.

There's a spiderant hive outside where the last recorder is located so you can head out and kill spiderants until you meet the necessary quota for the bonus objective.