Check out the following videos if you want to see how each of the Challenges are completed.
'Bare Hands' Challenge
Grab the grunts and use them as a battering ram. Try to knock the Cyclops of the ledge as it saves alot of time.
'Population Control' Challenge
Dont allow more than 50 enemies at the same time and keep pressing L1 + Square on enemies and grabbing them to use as a battering ram.
'El Matador - Ole' Challenge
Try not to get gored by the Minotaurs and don't get piled on by the enemies. Best way to do this is use the Square, Square, Triangle combo twice at the start to take out the first Minotaur and then use L1 + Square on the other enemies. At the stages where there are 2 and 3 Minotaurs go to the ledge and roll so you hang off (keep pressing X while moving left to right so you dont fall or climb up) and let the Minotaurs charge at you so they fall off and take other enemies.
Score 1,000 points by knocking enemies out of the arena. Simply beat up the big enemy at the start and climb onto him when the enemies spawn and keep hitting them using Square. Try to get the Minotaurs and Wraiths as much as possible as they are worth the most points.
'Hades' Kids' Challenge
Get 5 Cyclops to spawn. Best way to do this is to keep using the Square, Square, Trrangle combo and dodge their attacks by rolling. Finish them off when they have a Circle over their head.
'Simply Smashing' Challenge
Destroy the urns before the times runs out. This can be easily done by using Square to destroy while moving around quickly. Use roll when needed.
'Get Stoned' Challenge
As this is the hardest Challenge it is recommended that you try to get this one last. Allow the Gorgons to turn you into stone 10 times without dying, the easiest way to do this is to press Circle at a Gorgon at every opportunity so it gazes at you and then press L1 to reflect and press the wrong button so you turn into stone. Quickly break free by moving Left and Right rapdily and keep repeating this process and although you wil die several times you will eventually get the Gold trophy.
The following glitch will allow you to have ALL the weapons and items fully upgraded when you begin a game on any difficulty setting. To enable the glitch beat the game on any difficulty to unlock the 'Challenges of Olympus' feature and then complete ALL 7 Challenges of Olympus to unlock the Combat Arena. Start a round in the Combat Arena on Titan difficulty and if you now die in quick succession the game will ask if you want to switch to Easy mode. Select 'No' and start a game. This glitch is best used immediately before attempting Chaos mode.
It's actually a corection on the maxxed out weapons after the combat arena glitch I)it works only on difficulty levels you already have completed Ii)if you use something before it is to be used in the original game event series for example (break the judges and you go for the chain before you beat hades the ps3 lags and can't be turned off except from the button on the console and you may end up loading the same spot again and again) Iii)the chains of exile don't maxx out you get em from athena at zero exp
To perform this glitch you must first unlock the Combat Arena. Set the magic to infinite and get yourself killed in the Combat Arena 5 times so that the game asks if you want to switch to 'Easy' mode. Choose no and you will be returned to the 'Main' menu and when you now start a new game on whatever difficulty you were on during the Combat Arena you will begin the game with ALL weapons maxed out and infinite magic.
Collect the following Godly Possessions to gain the corresponding effect during bonus play (once you have beaten the game once). The Godly Possessions must be equipped in the 'Items' menu for their effect to become active and enabling them will disable cheats.
Daedalus' Schematics: Unlimited Item meter.
Hercules' Shoulder Guard: Decrease damage taken by 33%.
Aphrodite's Garter: Continue to use Athena's Blades.
Hermes' Coin: Collect 10 times the amount of Red Orbs.
Hephaestus' Ring: Automatically win ALL context sensitive attacks.
Helios' Shield: Triple the Hits counter (located to the right of where you kill Helios).
Poseidon's Conch Shell: Unlimited Magic (located in the chamber where you rescue the Poseidon Princess).
Hera's Chalice: Health meter slowly drains over time, but never completely emptying it (located to the left of where Hera falls in the garden).
Zeus' Eagle: Unlimited Rage of Sparta (climb the wall to the right of the Heart of Gaia and it is located on the ground in plain view)
Hades' Helm: Maximum Health, Magic, and Item meters (killing Hades and then jump into the River Styx, swim against the current down and to the right and it is located at the bottom of the river).