Just what it says - have a save with 100% completion.
To do this, you will need to:
Finish the story mode.
Solve ALL the riddlers challenges (Riddles, question mark puzzles, trophies, Spirit of Arkham stones, teeth smashed, audio logs and secret maps)
Get 3 stars in all the challenge rooms (though the extra content maps do not count which is annoying...)
UPDATE - sorry I should say that the final spirit of arkham is in the penetrntiary where you rescued the warden and got the cryto sequencer.
There are plenty of YouTube videos to help with the challenge rooms, and the riddles are fairly easy, especially when you get the map for each area.