Quick Description: The SSIS 2012 Transfer Database task fails with error code 0x80131500 (An error occurred while transferring data)
Error: The Execute method on the task returned error code 0x80131500 (An error occurred while transferring data. See the inner exception for details.). The Execute method must succeed, and indicate the result using an "out" parameter.
There are multiple things to check here:
Check all the paths are correct in the destination database section of the task. SSIS auto-populates this, but it isn't necessarily correct, and appears to just be the file locations of the source database. If those path don't exist on the target server, it will fail. See this thread for more information.
Check permissions to the data/log directories on the destination server for the machine account of the source server.
Verify you are not attempting to transfer from 2012 *to* an older version