Head east #1, glide onto the next building and quickly climb the roof. You can't get too far away or make big mistakes during this chase, as allowing the assassin to get too far away will end the mission. Keep following the ninja, avoiding any obstacles on the way. Soon you will have to make a new jump #2 towards the ledge in the distance.
Prepare for jumping onto the roof of the higher building in just a while #1. Run east, eventually reaching a ledge sticking out of the wall #2. Climb onto it and turn left.
Continue climbing up #1. Look out not to fall down, as even using the Grapnel Gun to save yourself might cause the assassin to run away. After reaching one of the higher ledges turn left again and jump towards the roof of the nearby building #2.
Run straight, jumping onto the roofs of the lower buildings #1. Luckily the chase will soon end #2, as the assassin will stop and start attacking you.
The fight will be very short, as the only thing you have to do is wait for the well-known signs to appear above her head #1 and perform a counterattack when it does (Y). The cutscene will show that Batman has manages to put a tracking device on her. Hear out a conversation with Robin, from whom you will receive the Line Launcher #2.