Easiest way to monitor something like this is to have Skype go through a proxy, then look at the proxy logs. Explaining how to install a Proxy and configure it is WAY outside of a Super User question/answer (I could write a book to cover the subject). You may be able to find proxy services on line that allow you to access the logs for your account. There are several proxies you can install on your own computer as well. Keep in mind, one may be a monthly fee, and you are responsible for the other.
This is an article from skype explaining how to access account history (phone call history).
The important part:
The Recent tab shows all of your most recent conversations and calls. To view a specific type of history – for example, just your text message history or just voice message – click View and then select from the menu what you want to look at.