The subway tunnels stay an open location of Arkham City throughout the whole game, though you won't be able to check out every its part at once. In order to reach the central station, you will need the Remote Electric Charge, while the eastern part of the tunnel require the Line Launcher.
In order to reach the tunnels, you can use either of the two possible entrances. In the beginning part of the game the better choice is using the western one (screen above), found in the Bowery, nearby the museum. Be careful however, as the area is likely to be patrolled by armed enemies.
The eastern entrance is in the Industrial District and it's a large hole into which you can jump (screen above). In this case you will have to look out for armed inmates as well.
Batman Trophies - 26
Riddles - 5
Joker Teeth - 12 (4 challenges)
Catwoman Trophies - 5