If you get the "Something Went Wrong" error when attempting to log in with your Microsoft account, your system's HOSTS file may contain something that blocks connections to XBOX/Microsoft account servers, or you are using a very old Badlion Client launcher version.
This guide is only for the error message shown above. Before following the instructions below, uninstall your current Badlion Client version, restart your computer, then go to https://client.badlion.net/, and download the newest version. If the same issue persists, you must follow the instructions below.
Resolving this issue
To resolve this issue, you first need to run Notepad as an administrator.
Click "File" and then "Open".
Locate the hosts file in the C:\Windows\System32\Drivers\etc folder and double-click on it.
Remove the lines that have live.com or xbox and 127.x.x.x in them.
Save the notepad file by pressing Ctrl+S.
Open Badlion Client and try logging in again.