Once you shoot the rope that holds the bridge (which is not necessary), grab the narrow ledge on the wall, but instead of jumping for the horizontal pole, use the Grapple to catch the ring above to the left.

Climb up the Grapple line and turn right to face the way you came. There is a ledge above the one you came from. Swing and jump to grab it. Then climb into the alcove with the switch.

Once you use the switch, exit from the other side and jump to grab the ledge of the wooden structure on your right. You can go and get the Cog #2, kill the two bats and shoot the bridge. Then go and get the Shotgun and Large Medipack.