This game is far easier and less complicated than its predecessor, requiring only two and a half playthroughs, which can be done on either Easy or Medium mode.

As long as you're following the guides in our Links page, the Platinum can be earned in roughly 15 hours or so.

For your first playthrough, you can select Easy if you wish. However, you'll eventually need a total kill count of 333 enemies across your playthroughs to obtain the Heather Beam. Since Easy mode doesn't have as many enemies, we recommend playing on Medium, otherwise you may need to do another playthrough later on. During this playthrough, focus on getting the Normal ending for the I'm Normal I Promise trophy. You can also go for the Hoarder trophy, by finding at least 100 items, as well as the Wall Basher for finding the silencer. Hopefully, and particularly if you're playing on Normal mode, you should also unlock the They Look Like Monster To You trophy for defeating at least 75 enemies.

For your second playthrough, we highly recommend playing on Medium if you haven't already, in order to get those kills. This time around, we recommend going for the Possessed ending to unlock the It Was All In Your Head trophy by having over 4000 points by the end of the game. Kill as many enemies as possible. You can adjust the number of bullets you pick up from the Options screen, by hitting the L1, R1, L2, and R2 buttons simultaneously to access the Special options menu, and go into Bullet Adjustment. This makes things easier and won't affect the trophies. Also, if you haven't done so in your first playthrough, make sure you kill the final boss with a melee weapon, in order to obtain the infinite submachinegun.

For your third - and hopefully final - playthrough, you'll want to aim for the UFO ending for the Coolest Dad Ever trophy, which means having the Heather Beam and killing 30 enemies with it before reaching your apartment. You'll need the total kill count of 333 enemies in order to unlock the Heather Beam. If you haven't gotten it already, then unfortunately you'll need to do another playthrough. Luckily, however, once you do have the Heather Beam, getting the UFO ending doesn't take very long. Also, since the UFO ending makes for a short game, you should also go for the Makes My Head Hurt trophy on this run, which is for completing the game in only 2 saves or less. It should be noted that selecting Continue after dying will count as a save.

IGN has a Walkthrough here:
http://www.ign.com/wikis/silent-hill-hd-collection/Silent_Hill_3_Walkthrough?objectid=0

And a text-based Walkthrough by Conquerer:
http://www.gamefaqs.com/ps2/561292-silent-hill-3/faqs/26762

nauGie has a detailed Trophy Guide here:
http://ps3trophies.com/forums/showwiki.php?title=PS3-Trophy-Guides:Silent-Hill-3-HD-Trophy-Guide

Kheapathic has a great Trophy Guide here:
http://www.playstationtrophies.org/game/silent-hill-3-hd/guide/

And a Trophy Guide by Platisfaction:
http://psnprofiles.com/guide/64-Silent-Hill-3-HD-Trophy-Guide

Finally, here's a basic Trophy List:
http://psnprofiles.com/trophies/1381-Silent-Hill-3-HD