Instructions
Head over to West Arkham after the confrontation with Poison Ivy and go to the Penitentiary. Ignore the guards and enter the Penitentiary. Beating them is not necessary. Ignore the 16 henchmen waiting in the next area as well, and move forward until you meet the Titans.
Defeat the two Titans. Concentrate on the Titans as they beat the henchmen around them by charging at you. While a Titan is charging, throw a Batarang at his head then evade. Climb on the Titan after he hits the wall and use him to attack the other boss. Repeat until both are defeated.
Face the Joker, the game's final major foe. Evade the Joker's swinging arms by running away in a clockwise motion. Defeat the minions that pop out after the Joker jumps to the background. Use your quick Batarangs to keep the thugs away from weapons. Use Evade and Takedowns to defeat the minions, and avoid being surrounded as you can get overwhelmed in a hurry.
Use the Joker's own explosive toys against his minions. Lead the minions towards the toys and after you hear a honking sound, use Evade to avoid the explosion. Batarangs can also take out these explosive toys.
Shoot your Ultra Batclaw at the Joker's back when he turns to face the chopper. Make sure all enemies are defeated or else you will be interrupted.
Hit the Joker's head with melee attacks to remove a third of his life bar. Repeat the process of evading him, defeating his minions, and striking him when he is vulnerable until his health bar is depleted.