EDIT: Credit to IEvil IMonkey and XBU Philippe.
Pausing will stop the timer. You can also quit to main menu, continue and get the achievement. You do not have to do this in one sitting.
Here's a video walkthrough. The full recording was about 56 minutes. Not sure if loading screens/cutscenes all count towards the 1 hour as there is no in-game stat/timer. Following this, you will get all story related achievements and I point out where and how to get most of the miscellaneous achievements. Some of them eat up precious time, so you may want to save the speedrun for a second playthrough and just get all the missable achievements out of the way first.