This achievement is awarded for completing the
Most Wanted mission, Gotham on Fire.
There are three firehouses in Gotham that will be on fire, one on each island. To find them, look for smoke or listen for the sound of fire.
Once you arrive at the firehouse, get in the Batmobile and press
to fire the power winch. You then have to press
so that the needle stays in the hightlighted area. This means it has to be tapped gently and carefully. Once you turn on the sprinkler system, the man behind this fire will burst out of the window, and start flying away.
Now you chase him in the Batmobile. Follow him as closely as you can, but avoid the fires he shoots down onto the road. On the right of your screen is his fuel meter. Once he empties his fuel, you will be prompted to press
twice, and hold the second time, to take him down. Once he's on the ground, start mashing the
button.
Do this three times and you will have one more villain safely locked away.
As Calex dEUS pointed out, it is possible for him to escape if you are not quick enough with the takedown. When you see his fuel running low, be extra careful not to let him out of your view.
If there's any way I can improve this, let me know in the comments. Thank and good luck!