If you've played any of the original God of War titles, then you should have a good idea of the difficulty level for acquiring the platinum for this game. In fact, Chains of Olympus is considered easier than GOW I, II, and III, since the collectibles are much easier to find, and the "Challenge of Hades" is a piece of cake compared to the previous "Challenges."

Overall, if you have experience with the GOW titles and manage to complete your first playthrough on Hard while acquiring all the collectibles and missable trophies, then it should only take roughly 10 hours to obtain the Platinum.

If you're in a rush for that Platinum, then start on Hard mode, which you'll need to complete for the Getting Your Money's Worth trophy. Along the way, you'll need to collect all 15 Gorgon Eyes, all 15 Phoenix Feathers, and upgrade all your weapons by unlocking all the chests you come across. Also, take not that there are 4 missable trophies: Two Girls One Spartan, Collateral Damage, Mutton For Punishment, and Old Softie. Check out the God of War Chains of Olympus trophy guide links under our Links tab for further details, and make multiple saves along the way to avoid having to replay the entire game should you miss one of those four trophies.

Once you've finished the game and collected nearly all the trophies, start a new game - on Easy, if you like - using an unlocked costume for the Cosplayer trophy. Don't worry, you needn't play the entire game again with this costume for the trophy - in less than a minute, you should hear that bling.

All that should be left is completing the "Challenge of Hades," for the Piece Of Cake trophy. Luckily, there are only 5 challenges, and are far easier than those challenges in the original God of War titles.

First, here's a Walkthrough on IGN:
http://www.ign.com/wikis/god-of-war-chains-of-olympus/Walkthrough

Here is a text-based Walkthrough, by Brad Russell:
http://www.ign.com/faqs/2008/god-of-war-origins-walkthrough-859334

And a great Walkthrough on Mahalo:
http://www.mahalo.com/god-of-war-chains-of-olympus-walkthrough/

This is a great Trophy Guide, by blazenarutoshippuden:
http://www.ps3trophies.org/game/god-of-war-chains-of-olympus/guide/

And another great Trophy Guide, this one by paperkup:
http://www.ps3trophies.com/forums/showwiki.php?title=PS3-Trophy-Guides:God-of-War:-Chains-of-Olympus-Trophy-Guide

Another useful Trophy Guide, compiled by several creators:
http://psnprofiles.com/guide/1025-God-of-War-Chains-of-Olympus

This Trophy Guide, by KFHEWUI, also contains links to Youtube videos demonstrating each of the Challenge of Hades:
http://www.gamespot.com/god-of-war-origins-collection/forum/chains-of-olympus-trophy-guide-spoilers-60338737/

Finally, here's a basic Trophy List:
http://www.ps3trophies.com/trophies/God-of-War-Chains-of-Olympus