How to easily obtain Cyclops Eyes.
First, ensure your Cronos' rage magic is fully upgraded to level three, this allows you to deal more damage and has a slightly longer stun time. Next, select treasures after returning to the main menu screen. Under the treasures will be a something called Challenge of the Titans. Challenge of the Titans is a series of different challenges, each having different objectives in order to complete them.
Choose the first Challenge, titled Blind Fury. It should be the only one unlocked if you've only recently completed the game without bonus play activated. Now, you need to take the Cyclops down using the specific take-down, which allows you to pull the Cyclops eye from it's socket.
The easiest way I found to do this, is to get Kratos to use Cronos' rage, effectively stunning the Beast Lords before they are able to climb onto the Cyclops. If you continue to use Cronos' rage (using one at a time is the most Magic efficient) the Cyclops will eventually weaken, usually when you have around 13-15 seconds remaining.
Press the correct button to initiate the mini-game and proceed by pressing the correct buttons until the cut-scene appears where Kratos pulls the Cyclops' eye out. This will make the count of Cyclops eyes you've collected go up by one. By completing this challenge, a screen will pop up asking you if you wish to save, to continue or to restart the challenge. Choose 'continue' to continue onto the next challenge.
Now for the supposedly fast part, allow Kratos to die in this challenge and return to the challenges list, selecting Blind Fury once again. Repeat the above instructions and your Cyclops Eye count will go up one again, it should not take too long using this method to obtain the 20 required eyes that unlock a new costume.
Note: You may not even need to continue onto the next challenge and then die, however I found that by restarting the challenge, or saving the progress and restarting only kept the Cyclops Eye count at the exact same that I started with.
Added by: Vindicator Jan 4th 2011, ID#33409