@eskimo: Your solution would be enough for me, if the parent directory would not be stored in the zip file. If the URL is .documentDirectory then the extracted zip includes a "Documents" folder. After some time of researching, I don't think, there is a solution for my problem. I don't want to use a big third party library, only to remove the "Documents" folder.

Thanks for you comment. I talked to the backend guys and they will accept nested files in a ZIP, so we don't need third party libraries.