Solved it. It took so long to figure out but here is how I got it to work.
Java Code on Server Side:
// Removed and added to Application Context
restletComponent.getDefaultHost().attachDefault(challengeAuthenticator);
Application Context:
<bean id="propertyConfigurer"
class="org.springframework.beans.factory.config.PropertyPlaceholderConfigurer">
<property name="locations">
<list>
<value>configuration.properties</value>
<value>log4j.properties</value>
</list>
</property>
</bean>
<bean id="config" class="Config class path location">
<property name="filePath" value="${Properties entry value}"/>
<property name="archivePath" value="${Properties entry value}"/>
<property name="username" value="${Properties entry value}"/>
<property name="password" value="${Properties entry value}"/>
</bean>
<!-- Restlet application -->
<bean id="application" class="Application class path location" scope="singleton">
<!-- Sets the router for the application -->
<property name="root" ref="router" />
<property name="config" ref="config" />
</bean>
<!-- Sets up the server -->
<bean id="server" class="org.restlet.ext.spring.SpringServer">
<constructor-arg value="${Properties entry value}" />
<constructor-arg value="${Properties entry value}" />
</bean>
<!-- Used to map routes to Restlet resources -->
<bean id="router" class="org.restlet.ext.spring.SpringRouter">
<property name="attachments">
<map>
<entry key="/getCompanies" value="Resource class path location" />
<entry key="/getList" value="Resource class path location" />
<entry key="/getFile" value="Resource class path location" />
<entry key="/archiveFile" value="Resource class path location" />
</map>
</property>
</bean>
<!-- Creates a restlet component that contains the server and attachs the application -->
<bean id="restletComponent" class="org.restlet.ext.spring.SpringComponent">
<!-- Sets the server in the Restlet component -->
<property name="server" ref="server" />
<!-- Attachs the application to the virtual host -->
<property name="defaultTarget" ref="application" />
<property name="defaultHost" ref="defaultHost" />
</bean>
<!-- Used to have login authentication for requests -->
<bean id="challengeAuthenticator" class="org.restlet.security.ChallengeAuthenticator">
<constructor-arg><null /></constructor-arg>
<!-- Sets the Challenge scheme parameter to the static class member -->
<constructor-arg value="#{ T(org.restlet.data.ChallengeScheme).HTTP_BASIC }" />
<constructor-arg value="GetWSRealm" />
<property name="next" ref="application" />
</bean>
<bean id="defaultHost" class="org.restlet.ext.spring.SpringHost">
<constructor-arg ref="restletComponent" />
<property name="defaultAttachment" ref="challengeAuthenticator" />
</bean>
Hope this helps others trying to get their application working. It took me a while to get this to work. :)