In this chapter, Batman dukes it out in the very theatre where his parents died, and tries to save the only woman he's ever loved.
Follow the homing tracker to the Monarch Theatre. The entire place is covered by no less than ten snipers, two of which are guarding the door to the theatre itself. Follow the route in the video and you should be okay, though. The real challenge is through that door, the final boss...but it's not Joker.
FINAL BOSS: Clayface
Clayface will remain in his clay form throughout the fight, so you don't need to worry about disguises. The first phase of the fight requires you to throw Freeze Blast grenades at him to damage him. Clayface is large, fast, and has a large variety of quick, damaging attacks. Throw the Freeze Blast grenades at him at every opportunity, and dodge his attacks. Once he's stunned, run up to him and beat him down. Batman will automatically grab Ra's' katana that is lodged in Clayface and slice him up with it. Repeat the process again.
Joker will then blow up the floor, and the final phase of the fight begins. Clayface will stand in the back of the room, much like Poison Ivy, throwing attacks at you while bits of himself, shaped as thugs, attack. You need to balance between taking out the clay enemies and actually damaging Clayface. The grey health bar represents how much health Clayface has, and the brown bar represents how much clay is left to form enemies before he needs to regroup. After you've thrown enough Freeze Blast bombs at Clayface, he will sit there, frozen, and you can run up to him and deliver the coup-de-grace. Congratulations, you've beaten Arkham City!