01: Batman's Last Case:
Press the view button to your list of objectives. Batman's Last Case should be at the top. Press A on it to view its objectives.
1.1 - Kirk Langstrom
Follow on-screen guide
1.2 - The Langstrom Drive
Follow on-screen guide
1.3 - Weird Science
Follow on-screen guide
1.4 - Blackgate Blues
Break into the prison, beat up some bad guys, speak to Harley Quinn; beat up some more bad guys, reach the basement, find the file, go back to Harley, chase the balloon by beating up bad guys. Once you grab the book, you'll be able to go back to the Belfry where you'll need to speak to Alfred.
HQ01: Harley Quinn
While still in the Belfry, simply go to the bulletin board and open Harley's book.
Once you complete this, you'll also unlock the "Har, Har, Har, Very Funny" Achievement.