Return the way you came to the Docking Platform and prepare for a fight. Head up the steps towards the Turret you hacked earlier and summon Eleanor to your side before the Alpha Series and Splicers attack. The entrance to the Infirmary is to the west, through the doors near the Turret.
Enter the Infirmary Wing and quickly hack the Security Camera on the right. Ignore the locked gates on the right for the Pediatric Ward and Quarantine Area for now and continue left, towards Ward A. Check the office on the left for ammo, then continue down the hall, past the patients’ rooms to Ward A.
Make your way through Wards A and B to the room beyond the locked gates you saw earlier. Press the button on the right to unlock the gate there, then continue left past the stairs leading up to the Pediatric Ward, and inspect the Quarantine Area. Summon Eleanor and press the button on the back of the column to open the cells. This frees a few Alpha Series to attack, but together with Eleanor and your Elite Security Bots, they shouldn’t pose a problem. Hit them with Incinerate! 2 (or charge it for a steady fire stream) and finish them off with Armor-Piercing Rounds or Frag Grenades.
Enter the last room in this area to locate the final Power to the People machine in Rapture, along with another Audio Diary. Search the cells and under the stairs for Heat-Seeking Rockets and other munitions, then climb the stairs to the second floor of the Infirmary.
Have the Hack Tool ready before you go through the door to the Surgery Room atop the steps—there’s a Security Camera across the room, pointed directly at the entrance.
Continue through the Surgery area upstairs and round the northeast corner to the right to enter another reception area. This safe is behind the counter, out of sight. There is a Security Bot Shutdown Panel just through the doors on the right, but it’s best to use an Auto-Hack Dart anyway. This can be a tough one to crack.