The circumstances of encountering the boss: Bird is a boss connected with the side mission concerning retrieving chemical weapon and stopping the gangs from fighting any longer. You confront this character at the very end of this mission, after you reach the main area of the My Alibi club [Dance Floor].
You can start the fight with Bird and his people in any way you want. They do not own guns and cannot, as a result, reach Batman. Personally, I recommend using the upgraded glue grenade, to hold the boss's most dangerous men, although you can also consider using the grapple, batarangs or the concussion detonator.
After the fighting starts, you should, first of all, note the two enemies wearing very heavy armors, with the green tubes sticking out of their backs. Avoid the charges of this kind of enemies and do not let them grab you. At first, attack then using the cape and a series of quick blows but, only if the shock gloves are available.
A quite useful bit of information is that Bird does not have any unique abilities, nor is he tougher, even though he has a separate health bar. This means that you do not need to pay too much attention to what he is doing and, first of all you should deal with the heavily armored enemies, who have been described above, as well as with the enemies with knives.
Ultimately, you need to eliminate all of the enemies on the dancing floor so, it is best to leave Bird for the very end. After you have depleted his entire health bar, approach him and press the interrogation key/button.