I found some posts that said to use Google Play Services. What about other platforms? Is their some libgdx library that I can use to implement it in core section or do I need to write separate score implementation to each platform?
Unless you know of a third-party service for leader boards that can be used on all devices, you'll have to write platform specific code. The wiki has a tutorial on that.
have you tried using App42 JAVA SDK? Here[http://api.shephertz.com/tutorial/Getting-Started-Java/?index=gs-javasdk&sdk=java] is the documentation for the same and then simply use leaderboard API documentation to implement leaderboards[http://api.shephertz.com/app42-docs/leaderboard-service/?sdk=java] in your libGDX games.