Bryan,
The Analytics API, which is part of the Genesys Cloud Platform API is your ticket to all of that:
https://developer.mypurecloud.com/api/rest/v2/analytics/. If you look in the panel on the left side of that page there are some specific topics that will probably interest you such as "Analytics Overview" and "Conversation Details Query" and "Conversation Details Job".
To get only completed conversations you'll need to use a segment filter to specify that you only want conversations that have an ending time.
If you want to actually play with the Analytics API then go to
https://developer.mypurecloud.com and in the "Tools" section click on the "Analytics Query Builder" and you can build and execute live queries against your org to make sure you are getting the results you expect before you start to write code.
If you have any question then please visit the Developer Forum at
https://developer.mypurecloud.com/forum.Good luck,
------------------------------
Jim Crespino
Senior Director, Developer Evangelism
Genesys
https://developer.genesys.com------------------------------