In Batman: Arkham City I've overheard several prisoners in the Bowery talking about a ringing telephone, saying that whoever answers it will die. Where can I find the phone in question?
This is a side-mission: there are several payphones throughout Arkham City, which have a random chance of ringing when you get close. They will be called out on your HUD. If you reach one in time (you can't be in combat, though it'll wait for you) you'll be able to advance the mission. If you miss a ringing phone, you won't be penalised; however, during the mission, you may have to pick up a phone before a timer expires, and missing this phone will penalise you.
As a hint, there's one Batman villain whose modus operandi involves making an innocent choice that leads to your inevitable demise/release. He also appeared in Arkham Asylum.
I found one in Park Row, northeast of the court house, under the overpass. Didn't realize it also gave me the Ring Ring achievement. From what I see, there are quite a few ringing phones to find.