Need a helping hand to setup domain mapping

Hi,

Can someone please help me to map http://bit.ly/1RZiygM domain name to http://bit.ly/1IC0Omi? (these threads pops up in Google search if I give domain names here. Please visit the bitly links to reveal domains)

* both URLs should work after the update. What I need is to direct http://bit.ly/1RZiygM domain name to http://bit.ly/1IC0Omi.

This is a WordPress multisite. I know there's a plugin to map the domains but I'm afraid to try that out. https://wordpress.org/plugins/wordpress-mu-domain-mapping/

I'm willing to provide admin credentials to the site and the Cpanel.

* Or else, please provide me detailed step by step instructions on how to do this.

Appreciate any help :slight_smile:
If this is out of your scope of support, please disregard this.
Thanks.