Instructions
Select the "System Update" icon from the PSP's XcrossMediaBar, or XMB, menu. This icon is on the far left of the menu.
Select "Update Via Internet" when the new page appears. Select your Internet connection from the list that displays. The DNS server error will not affect your PSP's ability to update its software.
Press the "X" button to begin the download of the new system software and press the "X" button again to install it when the download completes. Your PSP will automatically reboot. This will fix the DNS error when the PSP turns back on.