When the elevator stops, face forward. You will see a pair of thugs next to each other. Move in and put the new Double Assassination skill to use. Head forward a set of pillars from there and then over to the right. There is another Thug patrolling the area. As you approach he will be talking with someone. Use this to your advantage to quietly deal with them.
Head up the ramp to the back wall. Turn left there. You have another pair of Thugs to deal with using Double Assassination. If you need to restock your Smoke Bombs or Throwing Knives, turn around and head to the right of where you entered. Turn right to find a chest on the left-hand side. Open it for a quick restock. Head back to where the pair of Thugs were and jump into the room with the pipes and water.
Head forward and jump onto the pipe in front of you. Follow it to the left and then right. Keep moving in a run to jump forward and grab the bar. Evie should automatically swing forward. If not, there will be a prompt to guide you. Head forward and follow the walkway you are on. This leads to a second room with pipes you need to cross.
Run out onto the pipe and turn to the left. Jump onto the next and turn to the right. Once again, jump from there onto the bar and swing forward. This leads to the next room and gets you closer to Dr. Brewster. You can also go forward and Wall eject onto the pipes. Both paths lead to the same place. Just free run across to the raised walkway after the pipes to move forward. Head down this walkway with Eagle Vision to find and locate Dr. Brewster. Just keep going forward until Evie hops the pipe in her way. Go a bit farther from there to trigger the next cutscene with Brewster.