Towards the end of the game, you will get the "Heart Of Ice" side mission from Mr. Freeze. You must find Nora Fries to complete the quest. Go to the Industrial District in the south-eastern part of Arkham City. You should see a marked area of Nora's estimated location. There is a well guarded building with a locked front door. When standing in front of this building, fly north, and land on the ship. Use the Freeze Blast on the water to create a sheet of ice. Use the Batclaw to navigate to the destroyable wall, and use the Explosive Gel to get inside the building. Defeat the guards, and return to Mr. Freeze to get the "Bargaining Chip" achievement.

 

You must throw a remote controlled Batarang at the Mystery Watcher to get the "Catch" achievement. After rescuing Catwoman in the courthouse, exit the courthouse, and you should be able to see the Mystery Watcher across the street, on top of the building to your right. Simply throw the remote controlled Batarang at him, and he will automatically catch it, and you will get the "Catch" achievement. Note: You cannot get the "Catch" achievement after completing the Mystery Watcher side quest.

 

Successfully complete the main campaign to gain access to the "Restricted Area" at the center of Arkham City. You will then be able to climb the Wonder Tower, which is the tallest point in Arkham City. Climb it, jump off the tower, and glide towards the Church. You will eventually hit the invisible barrier between Arkham City and the restricted zone, and Batman will automatically turn around. To keep Batman gliding, simply turn around to hit the invisible barrier again and automatically turn around, lifting Batman up to continue his glide. If you keep turning and hitting the barrier, you will always remain in the air, and will get the "Gotham Base Jumper" achievement after one minute.