You should, of course, start by making it over onto one of the statues and taking a look at the current situation. In the swimming pool, there currently are eight armored enemies and the good news is that there are no enemies with the disrupting devices among them. You should try to use the vantage points to eliminate the enemies right from the beginning, because it will become impossible later throughout this scene. I recommend, of course, the inverted takedowns and using the upgraded grapple to pull the enemies towards the statues.
For the first time throughout the campaign mode, you will meet the enemies that carry mines here. After some time, they start planting explosive traps all around the place and it is worth remembering that you cannot step on one. Fortunately enough, mines can be detonated from afar, using the disruptor (the above screenshot), and it is worth doing that whenever there appears an enemy next to such mine.
Things get complicated at the moment when there are only four enemies left in the battlefield, because they will then arm the charges mounted onto the nearby statues. This means that you will have to give up using vantage points, because landing onto one will make it explode after several seconds.
Note - You can respond to the problem of inaccessible vantage points in a bit different way, and use the grapple to join two of them together with a rope. This will allow you to return to the rope and plan on attacks from there.
Blocking your access to the vantage points means, of course that you need to modify your tactics. For the purpose of moving around and planning on your actions, start using the venting shafts, both the ones under the floor and the ones joining individual rooms on the ground floor.
Use the detective vision to your aid, on a regular basis, to track the enemies down. When it comes to the recommended methods of their elimination, I suggest using the grapple to pull propane tanks and fire extinguishers towards them. Also you can try sneaking up from behind or waiting, while hidden behind a cover, for them to come, at which point you can press the takedown key/button. Eliminate all of the characters that have been staying at the swimming pool.
[New challenge: Campaign Challenge]
[New challenge: Custom Challenge]
You can now go to the ground floor and stop at the elevator to the apartment. Since the elevator is unavailable by default, use the Cryptographic Sequencer on the control panel and determine the correct password (the screenshot). After you reach the apartment, press the attack key/button several times to hit Joker and prepare to fight a full fight with Bane, which will start in the Penthouse Library.
[New Character Trophy: Bane]