This achievement isn't as hard as it sounds, I got it in my first playthrough back with the game after almost a decade, when starting the HD Collection. It seems daunting but it is doable.
I used this guide by GameFaqs user A l e x, to help me along:
http://www.gamefaqs.com/xbox360/632698-silent-hill-hd-collec...But honestly, I don't believe you'd even need that, I just wanted to make it easier on myself to get a few other achievements along the way, being my first time back to Silent Hill 2 in a long time. If you've played the game recently and are more comfortable with it, or you want to go for the speed run achievement ASAP, don't use this guide, as it'll waste a lot of your time telling you to going after unnecessary items, which makes it great for the Keen Eye achievement.
If you use a guide or not, Simply play the game and take things as slow or fast as your comfortable with, if you've played the game through a time or two before trying for this one you can breeze right through it, for sure.
Also, remember, you do have only 2 saves you can do through your playthrough, anything more then that and you won't get the achievement. Can't stress that enough. So make sure you have the time to play, cause if your forced to stop for some reason and have already used your saves up, your going to be pretty frustrated with yourself.
You'll also be frustrated if you take too many unnecessary risks when fighting, specially bosses (like trying to take too many shots when you should be running.. Or, like I did on Abstract Daddy, trying to use the Great Knife in a room the size of a tuna can...), and end up dying. Unless you've decided to use one of your 2 saves right before/close by a boss, or else your going to have to play through whole sections of the game to get back to that fight if you die. This is also pretty important if your also going for the "500 Damage Taken or Less" achievement, since if you take a bunch of damage and still survive, theres a good chance you won't get that achievement. Either way, this achievement + taking a lot of damage = bad idea.
Some may wonder when I believe the best times to save are, but honestly, from a personal standpoint, I feel that's really up to you, your judgement, and how much time you have to/want to play the game in one sitting.
For example, I used my first save when I got to the Silent Hill Historical Society, it was the goal I set for myself when I started the playthrough and when I got there I was really ready to be done playing for the night anyway.. BUT when I picked the game back up to finish it the next night I sort of wished I had waited a little later, when I got to the Labyrinth or even right after fighting the boss before the boat ride across the lake (I leave his name out because no achievements spoil who it is) to have saved for the first time. The section after where I did save really wasn't that long, and if I happened to die, I'd have to take the long run down the Historical Societies stairs again -- Not fun.
I used my second save before the boss I won't name, because I thought he was going to be a much bigger issue then he really turned out to be, since, if you know how to handle him, he goes down in just a few hits, which left me feeling like I had wasted my last save. Also, the boat achievement managed to make me very mad so I ended up having to restart back at that save and fight that fight a few times more then I really wanted to.
So neither of my saves felt all that helpful in the long run.
The thing about the the game is that it feels like it floods you with save points at the end, where as most of the beginning feels sparse -maybe its because there's a flood of bosses at the end, or maybe its got something to do with the metaphors behind the save points (how they crawl through your head, and you going deeper into your nightmare), I don't know though. Either way you go about it you really probably don't have to save once if your doing a speed run, and if you do I'd say maybe do it before the Labyrinth, if you think you'll get lost/run into Pyramid Head. If not wait till just after the Labyrinth and use it before Abstract Daddy or the boss I leave unnamed right after Daddy.
*** Credit for the mentioned guide goes to GameFaqs guide writer A l e x***
***Thanks to Sofarob and Angelr1pper for the heads up on the whole Brookhaven Hospital, Pyramid Head fall damage, thing. I've decided to removed it from the guide because it was basically (from what we've found) wrong and/or irrelevant, but you guys still more then deserve credit for the info***
***As of April 6th 2012, I've edited down the guide a little, as I said I would in the comments. Its mostly the same but I've found a place to mention the side notes I made in the main body, cutting down the length a little bit and making the overall flow easier.***