It worked! Did Microsoft fixed the error? Cause I didn't do anything special.
After two times getting the 0x80188308 error during the day, I "Check for updates" at night and, while it was downloading and preparing to install, I put the phone on charge and I fell asleep (40 minutes later). When I woke up in the morning, the "Install now" screen was there and it took almost 20 minutes on the Gear Screen and 20 more minutes to migrating data.
I didn't hard reset, I didn't soft reset, I didn't downgrade, I didn't used Recovery Tool.
My phone is a Lumia 820, I still with Amber and I use US for location. The battery was 100 percent because the phone was charging all the night.
The ones who was getting the 0x80188308 error, please, try again. I really hope the issue is fixed for everybody!
(sorry for my bad english)