Where in Arkham Asylum are the plans for Arkham City

The endings are completely randomized. You've seen 2 out of the 3 endings. The other hand that you may end up seeing is that of:

the Scarecrow.

Neither playing the game through on different difficulties nor acquisition of Riddles will affect what ending you receive. And far as players have been able to determine, it's either completely random, or it's based on variables obfuscated enough that the playerbase can't figure it out.

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.