While on the way to the First Lady's Aerodome, you'll be required to obtain the Shock Jockey vigor. To do this, you need to navigate through the Hall of Heroes, which is basically a series of waves against the soldiers of a man named Slate.
Make your way to the HoH, dealing with your standard enemies who will wield machine guns and melee weapons, as well as a Crow and Fireman or two.
Once at the HoH, you'll need to complete to areas, the Boxer Rebellion, and the Battle atWounded Knee. Both are exhibits made by Comstalk to show his conquest at each location, despite Slate and Booker saying he wasn't at either location. Again, both areas consist of gunners and melee enemies.
Once you finish both areas, you'll be able to proceed through The First Lady Memorial. Once at the end, you'll need to deal with a Patriot, a mecha-George Washington. You'll be able to use the newly learned mechanic of tears to being a machine gunner in to the world, use this and go to the opposite side of the room, and it should make quick work of the Patriot, as the back of them is the weak spot.
Continue through the area until you meet Slate, and fight off his waves of soldiers. There are 4 waves, each wave consisting of about 5 enemies. Once all waves are finished, proceed through the door on the bottom right side of the area.
Once you find Slate, you will then obtain Shock Jockey as promised.