reporting services (ssrs) prompts with username/password
Open your project/Solution in SSRS tool. Select the report properties (Right click on report project and select properties). Update 'Overwrite dataset' and 'Overwrite datasource' as True. Then go to your shared Datasource properties and select 'credentials' section. There you can select 'Use this username and password' option and set appropriate SQL Server credentials. Click ok and no more Prompting for credentials from frond end :)
There are actually two logins you deal with when it comes to reporting services.
The login to the database is to capture the data, it has nothing to do with the actual report itself. That login you used is sent to the database as the user / credentials being used to pull the report data.
This prompt you have a screen shot of, is the authentication to the report server, by default rs uses windows authentication so enter your domain\username with password.
If you do not like this default behavior you can change it, this guide should get you started: http://msdn.microsoft.com/en-us/library/cc281253.aspx
See this as well: http://msdn.microsoft.com/en-us/library/bb283249.aspx