Note the above solution is more detailed and a better solution overall, however as i am transferring every solution from PlaystationTrophies .Org trying to populate TT with more solutions, ill still be posting lower their solution.
There are only 2 places in the main game where you can rip out the eyes of Cyclops. One is where you topple over the Temple in the Bog of the Forgotten and the other is outside the Temple of Fates. You can either farm Cylcops Eyes there OR use the easier method by doing Challenge of the Titans 1 over and over until you have 20 eyes. Just remember to save and go back to the Challenge menu after every time you beat the Challenge or else your progress won't be saved.
Sutasu's tip
First you finish Challenge of the Titans, it will unlock Arena of Fates. There just pick infinite health and 1 Cyclops Berserker and turn respawn on. I found it a lot easier than fighting cyclops and the riders, who are usually trying to hit me or ride the dude. You also don't need to restart the challenge.
All credit goes to original authors at playstationtrophies.org, and this is merely updating truetrophy fans with these guides.
http://www.playstationtrophies.org/game/god-of-war-ii/trophy...