Way to unlock the mission: You get the opportunity to start this optional mission after you complete Case 1224-4: Helicopter Crash. A detailed description of this investigation has been provided in the chapter of this guide, entitled Casefile Report.
The beginning of the mission
At the very ending of the abovementioned interrogation, Batman will have to use the Cryptographic Sequencer to decode the transmission that the details on the bullet case led you. Position the crosshair within the orange circle, hold down the appropriate key/button and listen to the conversation with Deadshot. The criminal will inform you that he has taken a hostage and that he invites you to meet him at the Gotham Merchants bank.
Reach the Deadshot's staying place
You can now go to Deadshot's hideout, i.e. to the Gotham Merchants Bank, which you have visited earlier while completing one of the storyline missions. By way of reminder, the bank is in the southern part of The Bowery. To access the building, you do not need to enter from the rooftop, because it is way easier to get in through the main entrance .
Defeat Deadshot and his goons
Start by moving quickly to one of the vantage points. Do not worry about Deadshot's healthbar, because you do not need to attack this character straight away, as long as you do not make a mistake, you will not be spotted. Deadshot will, at first, patrol the bank's ground floor and, before you turn your attention to him, it is a good idea to eliminate all of his goons.
Since the description of the bank's main area has been provided in the chapter devoted to the main storyline, I will only remind you that it pays off to use to your advantage the vantage points, the weakened walls, venting shafts and fire extinguishers, which can be used to blind the enemies. I especially urge you to watch out while attacking the enemies patrolling the upper level, because the boss often turns around unexpectedly and changes positions. This means that without the necessary precautions, you can be easily spotted.
When it comes to Deadshot himself, he is, unfortunately, immune to many of Batman's attacks (e.g. the inverted takedowns), which means that you need to prove yourself with a larger dose of creativity during the attempts to deprive this character of his healthpoints. The best strategy consists in getting the boss from behind after flying down from the vantage point. Still, you should not restrict yourself to the quiet takedowns only , because Deadshot can quickly respond such attacks. Instead, right after you start the quiet takedown, additionally press the standard attack key/button, to initiate the Knockout Smash (the screenshot).
Since Deadshot is initially patrolling the upper balconies, you can also cling to the edges and grab the boss at the moment at which he is near the balustrade . As a result of a fall from high, Deadshot should lose quite a lot of health points.
Another good idea is to knock the boss unconscious, best by using a concussion detonator. After Deadshot fall onto the ground, run up and press the combination which finishes off the enemies. Regardless of the strategies that you adopt, always remember to escape, after each successful attack, onto the nearest vantage point, because you are incapable of depriving Deadshot of the entire healthbar at one shot.
After Deadshot loses around 2/5 of his healthbar, there will appear some more of his goons in the bank. This means that it is a good idea to discontinue the attacks on the boss, for the time being, and focus on eliminating all of the ones who have just arrived. Just like before, keep all precautions and attach care to eliminating the enemies one after another. You should also watch out for the enemies who came into the battle with a device which x-rays the vantage points in search for heat sources (the screenshot). As long as you are not equipped with an upgrade that allows you to hide Batman's presence, you need to run away from the statues when they are being scanned, to prevent being spotted.
You will reach the next phase at the moment wt which Deadshot has only 1/3 of his healthbar left. Also in this case, you need to take into account the fact that there will be new obstacles for you to overcome. First of all, try to locate and eliminate the enemy with the disruptor on his back, as quickly as possible (the antenna on his back), thanks to which you will be able to use again the detective vision, for tracking Deadshot and his goons.
Apart from that, you should watch out for the enemies that place mines around. You can ignore these traps or detonate them using Batman's gadgets. Deadshot should be occupying himself with patrolling the bank's ground floor, in the meantime. Unlike in the fight's previous phases, you do not need to wait until you deal with all of his men, although it is a good idea to do so, staying in his closest surroundings.
After you nearly deplete Deadshot's health bar, he should grab the hostage and start using him as a human shield. You need to be VERY careful to prevent causing the civilian's death, because this would mean failing the entire mission. Wait for Deadshot to turn back, glide quickly towards him and land somewhere next to him. Approach the boss (the screenshot) and press the quiet takedown key/button. This is the end of this mission.
[Character Profile Updated: Deadshot]
[New Character Trophy: Deadshot]
[New Concept Art: Deadshot]