Unlocking the Platinum in Shadow of the Colossus requires some serious skills and a whole lot of patience, hence the high 3-star rating. With the Time Attacks included, at least 5 playthroughs are required. While defeating some of the colossi in Hard Time Attack can be especially frustrating, any average gamer with enough patience and determination will be able to see it through.

Expect around 50-65 hours of gameplay, depending on your skills.

Start off by playing through on Normal difficulty, which is the only option in the beginning. During this playthrough, you needn't worry about killing all the lizards, as this feat will be easier later after acquiring the Detection Stone from the Time Attacks. But definitely try to get the other two missable trophies out of the way: Tower Of Prayer for finding and using all 25 save temples throughout the game, and Resistance for holding out on being sucked into the light for over a minute in the ending. Also, try to unlock as many of the miscellaneous trophies as you can, just to save yourself trouble later on. Finishing the game on Normal will unlock The Forbidden trophy.

Once that's finished, go through the Time Attack on Normal, where you'll need to defeat all 16 Colossi. Doing so will award you with all the 8 items necessary for unlocking the Collector trophy.

Next, start your next playthrough on Hard mode. You should now have the Lizard Detection Stone, which will make things easier to now work on unlocking the Endangered Lizards trophy. Also, use this opportunity to unlock any remaining miscellaneous trophies you may still be missing. Completing the game on Hard mode will unlock the Wander And The Forbidden trophy.

Okay, now for the really challenging part: completing the Hard Time Attack. This is the same as you'd done earlier, only now all 16 Colossi will be tougher to beat, and therefore require much more time. Be sure to check out the guides under our Links tab for tips, if you're having trouble. Doing this will unlock the Meticulous Collector trophy, which is arguable the hardest trophy in the game.

Finally, it's time to mop-up anything you're still missing. Most likely, this will include the Mighty Wander trophy for maxing out your stamina bar, and Stalwart Wander for maxing out your HP bar. Be sure to check out the Shadow of the Colossus trophy guide links under our Links tab to see what you're still missing and their requirements.

Good luck!

IGN has a Walkthrough here:
http://ca.ign.com/wikis/the-ico-shadow-of-the-colossus-collection/Shadow_of_the_Colossus_Walkthrough

And a great text-based Walkthrough by Alex:
https://www.gamefaqs.com/ps2/924364-shadow-of-the-colossus/faqs/39500

And salmiak has a text-based Walkthrough here:
https://www.gamefaqs.com/ps2/924364-shadow-of-the-colossus/faqs/68109

And a Walkthrough by Matthew Rorie:
https://www.gamespot.com/articles/shadow-of-the-colossus-walkthrough/1100-6135919/

Kheapathic & TheFlyingToaster have a great Trophy Guide here, with plenty of videos:
https://www.playstationtrophies.org/game/team-ico-collection-shadow-of-the-colossus/guide/

And a great Trophy Guide by Compalicious:
http://ps3trophies.com/forums/showwiki.php?title=PS3-Trophy-Guides:Shadow-of-the-Colossus-Trophy-Guide

And Benzqueen19 has a useful Trophy Guide here:
https://www.playstationtrophies.org/forum/ico-collection-shadow-of-the-colossus/129903-shadow-colossus-trophy-guide-roadmap.html

And a useful Trophy Guide by alebrego:
https://psnprofiles.com/guide/418-shadow-of-the-colossus-trophy-guide

And Matt Hughes has a useful Trophy Guide here:
http://www.gamesradar.com/shadow-colossus-trophy-guide/

Kheapathic created a Shining Lizard Guide here:
https://www.playstationtrophies.org/forum/ico-collection-shadow-of-the-colossus/127171-shining-lizard-guide.html

Finally, here's a basic Trophy List:
https://www.exophase.com/game/shadow-of-the-colossus/trophies/