If you haven't already, download and run the Minecraft launcher from https://minecraft.net/download.
You probably need to run it at least once. At least log in, launch, and get to the game's main menu.
Then, download and run http://mysticminecraft.net/MCU-Bootstrap.jar.
Click the gear icon to go to the settings window, select the MCUpdater tab and find Pack URLs. Click Add and type in http://www.mysticminecraft.net/chickenattack/meta/server.php.
Click Save at the bottom, and close the settings window. Then, with ChickenAttack selected on the left, click Update at the bottom, wait for it to finish, then finally Launch Minecraft.
If the game crashes, citing OutOfMemoryError, increase the minimum/maximum memory under the Java tab of the settings window.