Hint: Close the Enemy Spawning Pipes
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When you begin the second mission, you'll have a short time to kill all three enemies carrying viral containers. Two are in the sewer tunnels filled with water (and are found somewhat easily,) and one is in the large room with open pipes that continuously spawn enemies. After you kill all three viral container carriers, the clock will stop.
To reach the viral container in the large room, you'll need to cross a pipe hand-over-hand. This leaves you open to the constantly spawning enemies from the pipes.
To close the pipes, exit the large room by climbing the ladder on the wall adjacent to the platform where the viral container lies. Along the wall straight in front of you (or to the left as you head towards the end of the tunnel,) you'll find a room with generators and lots of enemies. Head up the steps in that room, and turn right in to the control room. There is a switch that you can hit (by pressing Triangle) that will close the pipes in the large sewer room. Head back, and you can collect the viral container without any trouble.