Approach the Declassify Skull on the wall to go through this section using Gnashers and Sawed-off Shotguns only. Climb out of the wall and continue outside. You'll encounter locust beastriders outside. Take them out and fight your way until you reach the Ascot House gate. Open it to continue to the next area.
Clear the mansion's courtyard then continue to the mansion's second exit. Before leaving and ending the section, grab the COG tag beside the stairs near the balcony.