MOST WANTED: Creature Of The Night (In progress)
Initially becomes available during Mission 06 - On The Arkham Knight's trail
Objective: Investigate the winged creature stalking the skies
Objective: Obtain a blood sample from the winged creature for analysis
Once you begin tracking the objective, any screeches the creature makes will show up a direction and distance away. Get up somewhere high on Miagani Island, and use your Batvision (detective mode) to help you find it. It will show as a bat shaped red flying thing as you view it in detective vision.
Approach it from above in a glide and Batman will do a Bat-Flying-Grapple to bring the creature down and drain some of it's blood to get it analyzed. Keep that glide technique in mind as you'll have to reuse in later sections of this sidequest and against serpent drones later in the story.
Objective: Search Dr. Kirk Langstrom's lab
Cross town to reach the marker showing the location of the lab, and go down the elevator (I was really expecting the Man-Bat to show up while it descended, but alas this is not a horror game). There is a screen here to watch which chronicles the events leading up to Langstrom's transformation, as well as his wife's body you can look at if you really want to.
Examine his computer, and it's time to play a little mini-game. There are two DNA strands, that at the bottom only one half of each is lit up. Both of these need to be clean (white) as they pass through the scanner for the percentage to increase. Anything else will decrease your percentage.
You control the strands (flip them) by tilting the left (left strand) and right sticks (right strand). When you see one side about to go green or yellow (respectively), flip it. Once you reach 100%, the mini-game will end and the cure will be synthesized.
Objective: Locate Man-Bat and administer the cure
Becomes available after completing Mission 10 - Infiltrating Stagg Airships
Man-Bat. See what they did there? Head to a high place on Bleake Island and have a listen for the screeches again. Once again, do the Bat Swoop Tackle, and get a free injection. Batman will need to do more though to finish the job.
Objective: Locate Man-Bat and administer the cure (again)
Becomes available after completing Mission 14 - Assault On Panessa Studios
Take to the skies of (you guessed it) Founder's Island in your search for the elusive Mannus-Battus. A swift glide takedown will return Dr. Langstrom to his original form and end his reign of ... slight inconvenience? *Shrugs* I guess Batman doesn't like similarly named competition.
Objective: Return Man-Bat to the GCPD lockup
Stuff him in the back of the Batmobile and zip off to the lockup to deliver him into the waiting arms of Gotham's finest. Oh, and a cell.