In order to reach 100%, you must:
-Finish Story Mode
-Obtain all gold bricks
-Obtain all red bricks
-Save all Citizens in Peril (both in gotham city and in each of the 15 levels)
-Unlock all characters (hero, villian, and bosses)
-Unlock all vehicles
-Get "Super Hero" in each of the 15 levels
-Must collect all 150 minikits (10 in each of the 15 levels)
The percentage counter (%) is available by hitting pause in the Gotham hub world, and will track your progress with each action you complete. Each gold brick is worth approximately 0.2%, so collecting them will count toward almost half of your overall completion percentage.
Anything I missed, or anything that needs to be added, please leave feedback.
EDIT: Thanks to ROBomination, you may not need to collect all of the vehicle for the achievement to pop. If any one else can verify, it would be much appreciated.