A better solution, which can be used for Both Building levels (Scene 6 and Scene 12) Is jumping up the building adjacent to the one the tree is located on. Since both Scene 6 and Scene 12 have identical building placements (Same types of buildings), You can simply jump up the side of the building and then jump to the tree.
You can see me doing this on Scene 6:
Sorry, this Game Clip has been removed
Essentially, stand on the ledge, jump and pull out, then re-land on the ledge above, you can see me moving up 2 floors at a time, if you are uncomfortable, move up 1 layer at a time. it's a simple repetitive motion, try and stay between the windows.