If you want, you can have an optional conversation with Mister Freeze. Turn on the Detective Mode back on and start looking for smaller blood stains, you should find one every couple meters #1. They will eventually lead you to the main museum exit #2.
Listen out to the conversation with Alfred regarding the drop off of the Line Launcher and head north #1. You of course still have to use the Detective Mode to locate the blood trails. After a few moments turn north-west and use the Grapnel Gun to reach the upper balcony #2.
Turn off the Detective Mode for a moment, as you will probably come across a couple enemies and you will have to take care of them #1. After finishing them off, once again start following the trail, eventually reaching the roof of the glass construction #2.
Now you will have to move north, defeating obstacles on your way #1. Remember not to hurry, as you might lose the trail otherwise. Soon you will have to jump down #2 and head north-east.
Stay cautious, as you might be spotted by the Thugs north of here #1 and you would have to take care of them before moving on. Turn east and climb onto the balustrade #2.
Jump down onto the glass roof below you, head east and use the Grapnel Gun to reach the balustrade above #1. Now you have to turn slightly north-east, choosing the alley between two buildings #2. After a few steps, turn north.
Jump onto the new balustrade and attack the new enemies by surprise #1. During this fight you have to look out for the ones equipped with knifes. After you're done with them, once again activate the Detective Mode and search for more trails, leading north-east #2.
Face the northern building and start climbing #1, helping yourself with the Grapnel Gun. Your goal is reaching the roof of this building and heading north #2.
Soon you will be forced to reach the upper part of the roof #1. Turn east and soon you should reach a point where the assassin's trail ends #2. Batman will suggest examining this place thoroughly.