After fighting past the Courtyard, head into the Gift Shop where you'll find a pair of kinetoscopes. Both are located near the vending machines. A third kinetoscope stands by the Gift Shop counter. Kill off the Motorized Patriot; try to circle around it so you can shoot its back.
After that, explore the area a bit more and locate a hairpin-locked door labeled "Maintenance Employees Only". Pick it open, take what you can and check the crate. Go back to the Courtyard to trigger the next fight. There is an RPG here; you can use them on the goons if you want but be sure to save some rounds for the Fireman and the Motorized Patriot.
After the fight, face the Slate's message on the wall and turn left toward an open door. In that workshop Voxophone along with a Health Infusion phial inside a green tool box.
Keep chasing Slate and killing his goons and you'll soon get to the end of his little game, where you can choose whether to kill or spare him. Your choice doesn't affect anything in the game. Snag the Shock Jockey Vigor and leave. Shock Tactics achievement / trophy unlocked.
Now for the next part, you must return to Soldier's Field and use the Shock Jockey to power up the Tesla coil for the gondola there. Watch out for goons on the way out of the exhibit for among them is a Crow. Upon exiting the Hall of Heroes, you will encounter some resistance. Have Elizabeth tear in the Mosquito then pick off the rest with the Sniper Rifle. Once the area is clear, proceed forward a bit and look along the left side and you should spot an inactive Tesla coil.
Power it up with Shock Jockey to gain access to a balcony and retrieve a Gear there. Keep going and once you get on the sky-lines over Soldier's Field, dismount on the hotel balcony with a dead Tesla coil. Power it up to enter the bedroom and secure the Voxophone and another Gear.
Once the gondola is activated, Comstock's men will come to attack in earnest and things can get pretty nasty. Your first priority is to locate the freight hook on the Soldier's Field Hotel and use it to gain leverage to board the flying enemy barge, where a Sniper Rifle and RPG are available for use. Kill off the Beast enemies on the barge first so you can pick off targets on the other ships in peace.
Make your way back to gondola after dealing with all the hostiles and ride it to the Zeppelin. Kill everyone in the aerodrome and board the ship. There is a Health Infusion phial on the desk inside the Zeppelin. Now, if you've been following the guide up until this point, this phial will max out Booker's health bar and give you the Raising the Bar achievement.
All future Infusions will henceforth be used to upgrade the Booker's shield and salt gauges. Use the control console. First Class Ticket achievement / trophy unlocked.