Go downstairs to encounter the Declassified Mission skull. For this section, serapede eggs that were left intact will hatch and spawn more serapedes for your team to eliminate.
There are 10 serapede egg clusters in the area and some of their locations change when you reload your last checkpoint. Make sure to check the corners and the ceilings to find them all. You should be able to spot all ten of 10 before opening the double-door. In case you checked every corner and you're still missing one cluster, restart the checkpoint and try again.
Head to the next room and repel the ticker and serapede attacks. Once done, head to the left to find a heavy weapon on the lift. Proceed while keeping to the left and you'll find a COG skull past Archive shelve XIII. In the dead-end there with a corpse and a dog tag.
Head to the other corner of the archives and a locust hole will appear ahead. Dig in and take out these flamer locusts. Enter the hole on the wall and regroup with your team mates to complete the section.