I have a java application running on a WebLogic 12c instance. I would to perform a mutual authentication with HttpsURLConnection but I didn't understand if I need to create a SSLSocketFactory (code side approach) and/or setup the "Two Way Client Cert Behavior" on the server of WebLogic (configuration approach). In this case, should the client certificate be imported into the weblogic or java keystore?
You should configure WebLogic for two-way SSL to enable a double authentication (client & server). This documentation explains how to achieve this.