Challenges are accessible via Treasures on the main menu after completing the game. There are seven of them, and in my opinion they vary widely in difficulty. Knowing what to do, and with some skill and a bit of luck, however, you shouldn't have too much trouble.
I found "Bare Hands" and "Get Stoned" to be the hardest / most luck-based, so I'd recommend leaving these two until last and getting the easier ones out of the way first. If you've played the previous
God of War games (I hadn't), then you'll know what to expect, and I've heard that
God of War III's challenges are easier than the previous two games' challenges.
If you need more help, I've included a YouTube video for each challenge below (credit goes to PowerPyx for those) as well as a few links to other walkthroughs regarding these challenges. Good luck!
1) Population ControlThankfully we begin with an easy challenge: you are armed with the Nemean Cestus (Hercules' weapon - those big massive gauntlets) and your goal is to prevent there being fifty enemies in the arena at any one time. This is more straightforward then it sounds: all you have to do is keep pressing the square button and work your way around the arena, killing as many enemies as you can - obviously fight through the larger concentrations of enemies if there are any. The number should average around late 30s/early 40s. Simply don't stop attacking, and you should get this first time through.
2) Bare HandsOne of the hardest challenges, you need to clear out a bunch of enemies within a strict time limit without any weapons. The only method of attack here is to grab the smaller guys (circle) and use them as a battering ram against the larger guys (square). Even when the larger guys are weakened, DO NOT initiate the button-prompt QTE minigame to finish them off, as you simply don't have time. Keep using enemies as battering rams and, once you've felled the three large enemies, you can instantly kill those remaining by grabbing them (again, circle) and splitting them in half (triangle). With luck, you can group the larger enemies together, or even knock them off the edge!
3) Get StonedPersonally I found this to be the hardest challenge. To get a Gorgon to stun you, try and grab it - it will recoil back and fire a green fog at you. Rotate the left analogue stick to break free after being turned to stone. You'll need to do this ten times, and a new enemy type is introduced in the small arena every two successful attempts, which means the arena quickly becomes crowded. When you're stunned, only one attack will kill you, and herein lies the main problem with this challenge.
Note that you can press circle to grab the small humanoid "opponents" that simply wander the arena to get a small amount of health. Do not fly into the Gorgon's green mist, as being turned to stone while in the air will instantly kill you when you land and break apart. Ultimately, you'll need a lot of luck to get through this.
4) El Matador - OleA relatively easy challenge, if you know how to approach it. PowerPyx's video (below) shows him grabbing the edge of the arena as the minotaurs approach him, so they charge over his head and off the edge of the arena. A fine strategy, but I prefer using L1 and circle to grapple towards and smash straight into them, which interrupts their charge. For the soldiers, L1 and square (repeatedly tap the latter button) has Kratos whirl his blades around him, pushing them back if not killing them entirely. Keep using this strategy until the last wave, where a bunch of minotaurs and soldiers attack at once: either use PowerPyx's method of hanging off the edge when the minotaurs close in to get rid of them first, or activate your Rage (L3 and R3 - click both analogue sticks in) and go to town on the minotaurs. Finish off the stragglers with L1 and square.
5) KnockoutBegin by immediately attacking the Cyclops as he spawns. Once he's down, follow the QTE minigame to get atop him. Now the fun begins. Simply walk around the arena bashing everyone you see. There's little strategy involved here (but a lot of luck); aim for the soldiers or larger concentrations of enemies, and go around the edges of the arena when possible. Eventually you'll complete this.
6) Hades' KidsAnother easy challenge; simply use the Plume of Prometheus attack (square, square, triangle) to deal massive damage to the Cyclops, as well as stunning them. Keep doing this until they die (you can always finish them off with the QTE minigame, if you'd like. With a bit of luck, you can even push them off the arena) and more will arrive. This challenge immediately ends when five Cyclops are in the arena at any one time. The trick here is to stun them so as to avoid being pushed off the arena yourself.
7) Simply SmashingThis is the last challenge, and surprisingly I personally found it one of the toughest ones; it is at least a short challenge, however. Work your way around the arena *tapping* square to extend your blade forward and break the vases. Do not initiate a combo, as it wastes very precious time. You'll eventually figure out an optimal route for this or get lucky.
For extra help, see these links:
http://www.gamesradar.com/god-of-war-iii-challenge-of-olympu...http://www.playstationlifestyle.net/2010/03/16/god-of-war-ii...http://www.gamefaqs.com/ps3/943928-god-of-war-iii/faqs/59390http://www.ps3trophies.org/forum/god-war-iii/42798-challenge...http://uk.ign.com/faqs/2010/god-of-war-iii-walkthrough-chall... (Challenge walkthrough is at the bottom of the page)