Talk with Fiona Wilson #1, who will tell you that since your last visit, the TYGER guards have taken over the tower. Start off by suing the Grapnel Gun to reach the nearest vantage point #2. There are eight enemies inside the room in total, three of them are snipers and they're the ones you should take care of first.
Start off by heading onto the vantage points on the left #1. Afterwards glide towards the first sniper patrolling the north-east corner of the room #2. Don't glide kick him, as it would alarm the whole room. Instead, land behind him.
Move in onto the first sniper mentioned above and silently take him down #1. Now you will have to act quick, so that you can eliminate the two other snipers before the enemies learn about it. You can use the fact that Hugo Strange won't be able to inform his goons that they're under attack until he doesn't officially end his speech. The second sniper is quite nearby, to the south #2.
After eliminating the second sniper, head even further to the south, but don't walk through the mined south-east corner, instead turn right and use the stairs #1. Wait for the third and last sniper above you to turn to around and go up the left stairs #2, therefore returning onto the upper balcony.
Now you can safely approach the third sniper and eliminate him #1. Afterwards take care of the five other enemies, who will be easy to neutralize without the sniper around #2.
Just like with the recent battle, you have to take into account that some enemies are equipped with proximity mines and they plant them from time to time #1. It's worth to upgrade the Disruptor so that you're able to remotely detonate the mines, though you can also stick with the traditional methods and attack from above (look out for the thermal goggles!) #2, using the grates on the lowest lever or using your gadgets. You have already secured this room previously in the game, so you shouldn't have a hard time navigating through it.
After securing the area, examine the middle part of the upper balconies to find an elevator entrance #1. Use the Cryptographic Sequencer on the control panel right of the elevator entrance and create a password (OBSESSIONS) #2.
Now you can enter the elevator. You will have to once again use the Cryptographic Sequencer (the panel is inside the elevator) and create yet another password (MEDICATION) #1. Wait for the elevator to take you to the upper level of the Miracle Tower #2 and get ready for action.
You have to quickly get out of the elevator, as the enemies on this level are expecting Batman's arrival and plan on opening fire when only the elevator open. Look up and use the Grapnel Gun #1. Carefully go forward and note that you're above the enemy units #2.
Glide forward and turn around to get behind the enemies' backs #1. You can act in multiple ways here, for example silently taking out one of the enemies or using the Disruptor on the guns. If you only have the chance, I'd recommend using the Freeze Cluster #2 to immobilize the enemies (you receive it for completing the Hot and Cold side mission).
Regardless of whether you have used the Freeze Cluster or not, your absolute priority is attacking the enemies equipped with firearms #1, who you should at least once blind with the Smoke Pellet. Only after eliminating them should you focus on the others, especially the ones with stun sticks #2. Traditionally leave the armoured one for the end.
After you're done, take out the Cryptographic Sequencer and hack the panel in the west corner #1 (SAFEGUARDING) #2.
Now you will be able to use the new passage which will take you north. After a few moments you will have to drop down #1 by, as you probably remember well, pressing the right rigger and A. Move right and don't let go of the cornice #2.
Stop after reaching the place where below you can see a little platform (north wall of the tower) #1 with an extension arm attached to it. Let go and look up. You have to use the Grapnel Gun to reach the platform on the upper level #2.
After getting up turn left and jump towards the extension arm in front of you #1. Afterwards pull up, turn right and head forward #2.
Now you will have to go round the whole Miracle Tower. Be careful, as one of the TYGER helicopters flying in the area might shoot a missile at you #1. In such case you must quickly back out, so that the missile hits the building and not Batman. Stop after reaching the western wall of the tower #2.
Look up and once again use the Grapnel Gun #1, this time to grab onto the extension arm above. Carefully move to its end, turn left and use the Grapnel Gun to grab the upper part of the steel construction #2.
Head towards the bigger platform #1, therefore ending the first part of the climb. Go left and after reaching the elevator shaft #2 dive onto the lower platform in front of you.
Head right and eventually you will reach a spot #1 where you will have to start climbing up again. Turn around and use the Grapnel Gun to reach the upper part of the construction #2.
Head forward and afterwards left, reaching the northern wall of the Miracle Tower. Look up and find the interactive platform which you will be able to grab using the Grapnel Gun #1. Climb up and note that you've reached a floor with a new elevator #2.
Take a look around the room to find a control panel #1 and of course hack it using the Cryptographic Sequencer. The password is MAINTENANCE #2.
A short hint on the next step will be displayed. Look up and use the Grapnel Gun to grab the ledge above you #1, thanks to which you will reach the Security Control Center. Keep following the only possible corridor and eventually you should reach a place where you can jump into a ventilation shaft #2.
The shaft can take you to two different places. If you decide to choose the branch on the same level #1, upon reaching the Security Control Center you will be inside one of the grates in the floor #2.
If you decide to follow the branch leading down #1, you will reach an exit in the building wall and after unlocking it you will be able to jump onto one of the outer balconies #2.
In order to complete finish the current objective, you will need to take care of all the enemies here, though there will be one additional difficulty here. In the middle part of the Security Control Center there's a room inside of which is Hugo Strange #1. If he notices you, he will inform all the guards of your presence #2. Luckily Strange's moves can be easily predicted and running to a safe place isn't very hard either.
The guards inside the Security Control Center can be eliminated in a variety of ways. The easiest is surprising them by hiding inside the grates in the floor #1, as well as approaching them from behind and silently taking out #2.
Note that the vantage points are outside the building #1, so it's best to use them as well as the numerous balconies #2 mainly for escaping when Batman gets spotted as well as for waiting for a good moment to sneak up on a guard from behind. Eliminate all the enemies to continue.
Now you can head onto the upper balconies and look for the entrance to the control room in which Hugo Strange is hiding #1. Use the Cryptographic Sequencer on the control panel and create the password GOTHAMSAVIOR #2.
A long cutscene with Hugo Strange and Ra's al Ghul #1 will start and end with a bang. Afterwards listen out to a conversation with the Oracle and watch Joker's message. #2. As you have probably guessed, your next objective is rescuing Talia al Ghul from Joker.