You can unlock this achievement by selecting a New Game from the main menu and playing through to the closing credits in a single sitting (no dashboarding, no loading another save, etc.). Oh, also there's the minor point of doing it without dying more than 5 times in the entire run. Here are some approaches to this achievement that I found useful:
1) Don't let the "complete the game in one sitting" part scare you. Once you know the solutions to all the puzzles, this game probably clocks in at about 1 hour and 20 minutes to complete. It's not like Dead Rising's "7 Day Survivor" where you have to set aside an entire day of your life. You may not unlock the achievement until your 3rd or 4th attempt, but still, at least you're able to do that over a couple of days.
2) If you die at all before Chapter 10 (the chapter where you're trying to outrun the flooding water), just restart your run. Chapter 10 is only about 20 minutes into the game, and those first 9 chapters are some of the easiest puzzles in the game. Unless you were doing something silly, there's really no excuse for dying that soon.
3) Once you get into the Chapter 10 range or maybe a bit later, NEVER restart your run until you officially hit 6 deaths. First of all, you never know what might happen. You might die 4 times in Chapter 16, but totally luck out on those jumps in Chapter 23, and that'll end up being the run where you get the achievement. Even if you continue playing and don't get the achievement, the additional practice on the later levels will only make life easier for your next attempt.
4) Chapters 12, 23, and 24 all have timing based jumps that you may want to perfect through Chapter Select before you start a legitimate attempt. I personally found some jumps in Chapters 13, 14, and 18 tricky.
If you need any more help, here are some videos with annotated tips I've uploaded to YouTube of my 2nd "No Point in Dying" playthrough. You'll probably want to click on each video to watch them directly through YouTube, as the annotations can be tough to read through an embedded player.