To capture an enemy, you must shoot them with a tranquilizer gun (rifle or pistol). Not many contracts actually require you to capture enemies, so this will take a while, especially since you cannot just capture enemies when the mission states you must kill them. The EASIEST way to work towards 500 captures is to tranquilize all enemies in missions where you get ambushed. You know you are getting ambushed when a message pops up as soon as you load into a mission. In these missions, the contract requirements go out the window, allowing you to tranquilize anyone. This achievement is also glitched for the good, it unlocked for me at around only 125 captures. You can check your progress in the stats under "Total Captured."