After getting inside Abstergo, you'll find yourself in a long hallway with glass walls. There will be researchers all over watching you. Make your way directly ahead until a couple of Security Guards appear to stop you. Combat with the guards in Abstergo is going to be very similar to the combat at the Stadium except there's going to be a LOT more combat here. Kill the few guards here and remember to watch out for their pistol attacks.
With your first few guards down, make for the elevator beyond them and get on. When the elevator stops, you'll have to get out and climb. You'll see a large window overlooking the room below. If you climb up the left side of the window, you can use the large rivets to climb up. Climb up the left side and then the right side of the window. Hop back left and then start climbing up and left to move around the elevator shaft. At the top, a guard will be waiting for you.
Assassinate the guard at the top and then fight the two other guards here. Turn left and go through the door at the end on the right. You'll come to a room with a large table and a lot of chairs. Inside will be two more guards. Kill them and exit into the next area. You'll be in some kind of indoor park area and you'll be on bridges on the upper level. Make your way across the bridges and kill the guards as you go. When you've killed them all, go the end of the bridges and through the broken window. You'll enter a hallway and to the left will be a door that may look familiar. Go through that door to confront Cross.
After Cross has a mental breakdown, chase after him. He will lead you back out into the hallway where there will be guards waiting for you. Head further down the hall and follow him to the right. Keep following him until he leads you back to the cubicle room. Below you will be countless rooms with animus machines and offices. Run forward along this path and you should see Cross ahead. Go as far forward as you can and then turn right. Climb down to the lower levels to resume your search for Cross.
Down here, you need to be careful of all the guards. Stay up on the cubicles and use Eagle Vision to help you find Cross standing on top of one of the cubicles. Continue to chase him down to the lower level and close the gap to assassinate him. With him out of the way, you'll have his gun to help you which is used like you would handle one in the animus.
You'll take the elevator up to the top floor. At the top, there will be a few more guards waiting for you. Kill them and work your way to Vidic's office.
After the event in Vidic's office, you'll have to work your way out of the tower. You can hit almost any button to use the powers of the Apple. Using the Apple, kill anybody who tries to stop you from leaving.
