Way to unlock the mission: You get the opportunity to unlock this mission some time after you have completed the game's campaign mode. Wait until Captain Gordon calls Batman and asks help arresting twenty criminals who have escaped the prison.
Beginning of the mission
As already mentioned, you need to arrest 20 various people and you can reach them in any order you wish. The whereabouts of the individual inmates are displayed on the world map although, you can just as well use the side0missions menu shown in the above screenshot and "visit them" basing on that list.
Arresting the escaped prisoners
The individual arrests do not differ in any particular aspect. Each time, you need to reach the place that the game points you to, find the escapee and several of his companions.
To the extent possible, always go for a surprise attack and try to eliminate at least one enemy at the outset. Fortunately, the fights in this mission are not too difficult, especially that Batman already has the shock gloves at his disposal. The prisoner himself is best left for the end because, each one of the escapees gives up after being defeated.
As a reward for arresting each prisoner (apart from the experience points for winning the fight), you receive a bonus of 5000 experience points. Arresting all 20 prisoners means, in turn, a bonus of 50000 experience points. Listen to the final conversation with Captain Gordon, which officially ends this mission.