Botanical Gardens--Part 1

Pick Up Harley Quinn's Fingerprint Trail in the Botanical Gardens

With Quinn taken care of, proceed through any of the three doors on the north side to find a Secrets Map, then exit the room via the door you entered through. Now follow your map to exit into Arkham West, then from there, head through the abandoned tunnel the Botanical Gardens in Arkham East.

Track Harley Quinn's Movements to Locate Titan Production Facility

Once inside the Botanical Gardens, you'll find two armed guards by a locked door. Take them down then use the Sequencer on the security panel to deactivate the electric fence, allowing you to proceed through the door into the Botanical Glasshouse.

The Botanical Glasshouse is home to six armed guards, but thankfully the room in lined with gargoyles which helps immensely. Go ahead and grapple to one of them and plan your attack. You have several options, dependent on which abilities you've unlocked. If you're patient, you can simply wait for the guards to spread out, then take them down one-by-one with a glide kick + ground takedown combo whenever you find a guard all by himself. Now keep in mind that the other guards will be alerted to your presence shortly after each kill, so immediately return to a gargoyle afterward for protection. Speaking of which, if you've unlocked the Inverted Takedown, you may want to hang from the gargoyle just above your kill, ready to grab an enemy as they pass by underneath. Once you've cleared the room, proceed through the northern door into the Flood Corridor, where you'll find the Joker.