Windows 8.1 request to "Enter your most recent password"... Legitimate?

Solution 1:

That's legitimate. You are logged with a Microsoft account (hotmail.com, live.com, outlook.com, etc). The password of your Microsoft account has changed since the last time you logged into this machine. Now that your machine woke up and got connected to the internet, it was notified that the password has changed, and it is asking you to enter the latest password, so other services that depend from this account are not interrupted, like Skype, Widnows settings synchronization, some Windows Store Apps, etc.