"Find second record" is a mission objective in the side mission "Sub-Level 13: Part 2" in Borderlands: The Pre-Sequel
Contents
Walkthrough
Just after the recording finishes a Tork bursts out of the nearby ventilation grate. Take it out and then you need to get inside that shaft. Head over to it and jump then crouch to get in. Follow it along to the far end of the tunnel. When you find the first drop, take it. Turn to the North when you land. You will find the second record.