Blue Recovery screen after Anniversary Update

Most suffering blue or black screens after this Update are able to get into Safe Mode and do the necessary repairs.  In your case it needs an AMD driver Update for the chipset or Display. 

Use whichever method works to Access Advanced Startup Options in Windows 8 or 10.   If none of the other methods work it may be necessary to Use a   Recovery drive or  Create Windows 10 Installation Media on another PC to boot using the  BIOS Boot Menu Key, choose the boot device as a UEFI device if offered, then on second screen choose Repair Your Computer

In the Advanced Startup options try (in this order) automated Startup Repair, System restore, then if necessary from Startup Settings try to get into Safe Mode with Networking, or lastly Safe Mode.

From Safe Mode w/Networking Type Update in Start Search box to Check For and expedite Updates that may be critical but are taking their time to install. Right click Start button to open Device Manager, import any missing or erroring drivers from the PC or Device's Support Downloads webpage.  How to: Install and Update drivers in Windows 10 - Microsoft Community.  In this case focus on AMD drivers for the chipset (if applicable) or more likely the Display.  If the PC's Support Downloads don't provide a Windows 10 driver, try 8.1, 8 and 7 in that order.    If those fail try AMD Driver Autodetect .  Report back for help if needed.

If Safe Mode is stable the problem is most likely drivers, but could also need disinfection, System file repair or repair of the image.  Most of the Upgrade problems seen are corruption passed from the old OS.  

Download, install, decline trial version, update, then run full scans with  Malwarebytes  and  AdwCleaner.

Uninstall any bloatware anti-virus like Norton, McAfee, AVG or Avast, enable built-in Defender to test performance.  Use the special  Uninstallers (removal tools) for common antivirus software - ESET Knowledgebase.

Right click the Task Bar to open Task Manager, on Startup tab disable everything until your install stabilizes, then only restore those you know for sure you absolutely need starting with Windows – none of them really need to unless you want them.   Also type msconfig in Start Search, in System Configuration on the Services tab, tick the box to Hide all MS Services, then uncheck everything.  Save and restart. 

If it still won't start or perform correctly, from the Advanced Options Command Prompt, or within Safe Mode accessing an  Elevated Command Prompt,  Copy and Paste or type each of these commands, each followed by Enter: 

sfc /scannow
 
Dism /Online /Cleanup-Image /RestoreHealth

If it prompts for Sources file, mount or insert Windows 10 installation media, locate install.wim or .esd file in Sources folder, substitute it’s path in the following command (for example: Dism /Online /Cleanup-Image /RestoreHealth /Source:wim:H:\Sources\Install.wim:1):  

Dism /Online /Cleanup-Image /RestoreHealth /Source:wim:Full Path to install.wim file:1

(or)  Dism /Online /Cleanup-Image /RestoreHealth /Source:esd:Full Path to install.esd file:1

sfc/ scannow

Exit

If at any time you are returned enough functionality but still have problems with an app then  Troubleshoot problems with an app - Windows Help .

If Safe Mode doesn’t work or help stabilize things then return to  Advanced Startup Options in Windows 8 or 10. Next try Command Prompt  to run above commands including sfc /scannow, to see if it will repair and start, or  Reset Windows 10.

Better yet do the vastly superior  Clean Install Windows 10 following the steps in the link to delete all partitions down to Unallocated Space to get it cleanest.  After install reactivate with your Product Key, automatically from embedded Product Key if a factory install,  or if free Upgrade has already activated. Activation in Windows 10 - Windows Help.

At any time you can  Rescue Files when Windows Won’t Start, use a Linux disk, or  Paragon Rescue Kit Free EditionFile Recovery Wizard to copy files to USB flash stick or an external or another hard drive.   

If these fail you can try to run Factory Recovery from it’s hotkey at boot; find yours by googling the “PC make/model + Run Factory Recovery.”    Factory Recovery methods 

Feel free to ask back any questions and keep us posted on how it goes.