I'm not going to write a walkthrough for each of the roughly twenty militia checkpoints, but will give an overview/tips to completing the mission.
Thanks to good Super man for this map of checkpoint locations! -
(From Hydrolex the map is missing 1 checkpoint on bleake island. there are 4 and your map shows only 3.
the missing one is left of oracles clock tower and right of the perdition bridge. roughly you can say its on the lower left side. moving there you should find it.)
The checkpoints will need to be unlocked by playing through the main story campaign (you won't get all of them unlocked until after 90% of the main campaign is completed), and will be identifiable by the large red barriers with the Arkham Knight's symbol on them. The goal is to take down all the militia soldiers inside of them, and then identify the checkpoint commander with detective vision to find his body and pick up and destroy his command radio.
As you progress in the story, the checkpoints will become increasingly more difficult to clear: they start with just simple batches of villains, and then will start to incorporate small sentry guns that you will need to blind with your remote hacking device. Some will have giant sentry guns that you will need to destroy with the Batmobile, which means either finding a ramp to launch yourself into the area, or using detective vision to identify an electronically-locked door which you will need to hack open to give your Batmobile access to the inside of the compound, allowing you to shoot down the giant turrets.
It is always a good idea to scope out the checkpoint before attacking, using your disruptor to sabotage any medics, chain gun brutes, or drone pilots. Take your time, play it smart, and eliminate the threats.
If you're going to downvote, at least tell me what I can do better.