Choose the door in the north-west part of the Loading Bay (Death Ride) #1. You can follow the hint and scan the currently unobtainable trophies (by holding LB) or just pass by and head to the next door #2. They lead to the Assembly Line.
Note that inside the room south of here there are three armed enemies. Theoretically you could reach them by jumping through the glass (or blowing it up using the explosive gel) #1, but it's much better to use an alternative route and surprise them. Jump onto the assembly line and find the switch in the east part of the room #2.
Crouch and choose the newly unlocked passage. You will have to use the Grapnel Gun to reach the upper balcony #1. After finding yourself back beside the room with enemies, once again fire Grapnel Gun, this time aiming at one of the vantage points #2. I'd now suggest spending some time in Detective Mode, watching the enemies' behaviour.
Note that one of the bandits is standing alone, he should be our first target. Use the local vantage points to get behind the backs of the characters below #1 and carefully jump down. Crouch and approach the previously mentioned lonely guard #2. Press Y to silently take him down.
Stay where you are and approach the two other guards who are standing beside each other #1. Press Y here as well, eliminating them both at the same time. Now you can head towards the west door. They're locked, so jump trough one of the local windows (lean out the analog stick towards it and press A twice) #2.
Use the nearest door leading to the further part of the Steel Mill #1, the Smelting Chamber. Note that you have reached a room with new thugs and a hostage, so you have to plan your moves carefully. Start off by crouching and wait for the guards on the nearby balcony to stand beside each other #2. Approach them and press Y to take them both down.
Now it would be good to use the Grapnel Gun and reach one of the nearby vantage points. There are four enemies left to take care of and I'd suggest beginning with the one patrolling the upper balconies #1. Jump down at the proper place to find yourself behind the guard's back and silently take him down in the well known way #2.
The second enemy is, for a change, patrolling the lower floor of the chamber #1. Just like before, jump down and attack him by surprise #2. Quickly return to the vantage point, as one of the bandits guarding the hostage will note the disappearance of his buddies that you have eliminated.
The thug mentioned above will exit the room where the hostage is #1. It would be good to eliminate his fast, so that he doesn't reach the bodies of the enemies you have taken down a moment ago. You have many options here, you can either use the Batarang, attack from above or wait for him to get below a vantage point and use the Inverted Takedown #2.
Now you have just one more enemy left to eliminate, the one inside the room with the hostage. The easiest way of surprising him is landing on the balcony and waiting for the thug to stand beside the window #1, through you could as well go through the ventilation shafts or reach the fragile ceiling part above the room. If you have chosen the solution I suggested, press Y as soon as you get a chance #2.
Now you can enter the room where doctor Stacy Baker is and free her (A) #1. Hear out some new conversations and note that you have gained a new and very useful gadget - the Remote Electric Charge #2. I'd suggest acquainting with it (Waynetech), as it has a couple different modes.