Deploy NextReports Server on WebLogic 12c

First, you should create a nextreports-server.war folder and unarchive the war file here.

Inside nextreports-server.war/WEB-INFyou should add weblogic.xml file:

<?xml version="1.0" encoding="UTF-8"?>
<wls:weblogic-web-app
        xmlns:wls="http://xmlns.oracle.com/weblogic/weblogic-web-app"
        xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
        xsi:schemaLocation="http://java.sun.com/xml/ns/javaee
        http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd
        http://xmlns.oracle.com/weblogic/weblogic-web-app
        http://xmlns.oracle.com/weblogic/weblogic-web-app/1.1/weblogic-web-app.xsd">

          <wls:weblogic-version>12c</wls:weblogic-version>
 
          <wls:jsp-descriptor>
             <wls:debug>true</wls:debug>
          </wls:jsp-descriptor>
 
          <wls:container-descriptor>
             <wls:prefer-application-packages>
                <wls:package-name>org.joda.time.*</wls:package-name>
             </wls:prefer-application-packages>
          </wls:container-descriptor>

</wls:weblogic-web-app>

Here we specified we want another joda library than that used by weblogic.

Next, we have to register reports folder as a web context. We create a reports.war folder as a sibling to nextreports-server.war, and inside it we have a WEB-INF folder with two files:  
web.xml

<?xml version="1.0" encoding="UTF-8"?>
<web-app 
 xmlns="http://java.sun.com/xml/ns/j2ee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
 xsi:schemaLocation="http://java.sun.com/xml/ns/j2ee http://java.sun.com/xml/ns/j2ee/web-app_2_4.xsd">
</web-app>

and weblogic.xml where we specified local path to our reports folder:

<!DOCTYPE weblogic-web-app PUBLIC "-//BEA Systems, Inc.//DTD Web Application 8.1//EN" "http://www.bea.com/servers/wls810/dtd/weblogic-web-jar.dtd">

<weblogic-web-app>

         <container-descriptor>
             <index-directory-enabled>true</index-directory-enabled>
         </container-descriptor>

         <virtual-directory-mapping>
             <local-path>/appsvr/reports</local-path>
             <url-pattern>*</url-pattern>
         </virtual-directory-mapping>

         <context-root>/reports</context-root>

</weblogic-web-app>

After your server starts, you should accordingly modify your server settings like base url, reports url , mail server and so on.

References:
Publish static context to WebLogic