There are a few Requirements for this achievement they are as follows:
1. Locate CT’s side quest this is the speech bubble left of screen in the
Swamp next to tunnel from the
East of Gotham.
2. Complete CT’s side quest
3. Unlock Chang Tzu (CT)
4. Purchase CT at cost of 500,000 studs
Ok the location of CT is just through the tunnel from the
East of Gotham in the
Swamp not the
“Hall of Doom”, it is on the higher ground so you will need to fly upto it.
Now you need to accept the quest and collect 3 lots of items highlighted on the map, they will be smashable objects which will be shown on the left side of your screen.
Now return back to CT and put these items into the machine next to CT.
Once you have done the above speak with CT and then you have unlocked him.
Now you need to purchase him for 500,000 studs.
As soon as you have done this select him as your coop AI character, then with your main player press

next to CT and press

to take a selfie with him as seen below:
As soon as this is done pop achievement unlocked.
Congratulations!
Happy Hunting