Edit: From comments, it seems you don't need to shoot the bird to get this, only crash the stock manually and then follow the fired banker story.
For those who want a short solution: Crash the stock manually in the stock room whilst disguised as an investor. Follow the fired banker mission story to kill the target by pushing her out of the window. Finish main objectives and exit via the window by the conference room whilst dressed as the fired banker.
Original solution (just disregard bringing a sniper and shooting the bird):
Okay, so this only has a few steps but was confusing to work out. To start out, finish the mission once so you can bring in a sniper rifle through an ICA drop point.
You now have 2 main steps to do:
1) Kill the target by pushing her out of the window in her office where she patrols.
2) Crash the stock.
I started with the stock as I wasn't sure if it needed to be done in any particular order. You need to disguise yourself as an investor (or start as one if your Mastery Level is high enough) and interact with the computer in the stock room and sell it off to crash the stock.
To kill the target by pushing her out of the window (you need to do this), follow the mission story for the fired banker (as you need his disguise for this exit to appear) and go up to her office. Since I crashed the stock first, she was still downstairs, so I took out all 3 guards in here and hid them behind the white sofa on the left so I would have the room to myself after I killed the target.
Once the target starts talking to you, she will eventually go to the window and face away from you, push her out and unpack your sniper rifle.
Here's where a sidestep comes in that will open up the scenic exit. Look across the room from the window and you will see a bird flying in a circle. Line up your shot and kill it.
Now all you need to do is either get the data core (which you can hide in the briefcase your sniper was in) or get all 3 back-up bits of data.
Once the main objectives are complete, you will see a new 5th exit on the map. This one is on the stairs leading to the top floor where the target was (by the conference room), where you can now exit via the window.
For reference, here is a clip showing the exit: