it's working now on my windows 8.1 the skype on desktop and the metro UI
1- you need to go to control panel and check for update ( make your pc up to date ) download all the updates
2- go to http://www.skype.com/en/download-skype/skype-for-computer/ and download Skype
3- restart your PC and Skype desktop should works fine on your windows 8.1 desktop
now for the metro make sure that you are closing all other metro apps and make the biggest space for your Skype metro app so he don't crash and if your system is 32 bit
try the 64 bit he will works that depend on your RAM space