Microsoft has given some advice for those running into the 800705B4 update error. This error is experienced by some users who trying to update their Windows Phone handset. Here is the solution to it.
First, make a backup of all the media stored on your computer. Then, erase all content. Do this by going to “Settings” > “Phone” > “Sync Options” > “Erase All Content”. Then try the update again and it should go smoothly.
Once the update has been successfully applied, you can restore your media back, including the apps that you downloaded / purchased. For the records, this is what the error says
There was an error while trying to update your device with the latest software.
Please try again.