Once you get off the helicopter in the beginning of a new game you can just sit there for 2 hours to unlock this achievement, just keep your game from pausing.
Note: The Xbox 360 version glitch does not seem to work as I attempted it, if anyone does figure out a way to make it work comment or PM me so I can update this guide but I did as follows:
*** Spoiler - click to reveal ***(pulled from Makker's 360 guide)
1. Start a new game in 72 Hour Mode.
2. When the chopper drops you off, walk into the door next to Carlito.
3. Go through the Security Room and out into the mall (Entrance Plaza).
4. At this point you get the cutscene where you first see Brad and you're told to get something to help barricade the door. Instead of doing this I just stood by the window on the balcony overlooking the car park outside and waited for my Indoorsman achievement to pop.
5. Once Indoorsman has unlocked, return to the Security Room the way you came and save your game on the couch provided.
6. When it then pops up advising that the game has saved successfully and asking if you want to continue playing, turn your Xbox off (I used the guide button but I expect it'd make no difference using the 360s power button or a remote control).
(I quit out of dead rising and power reset my Xbox One)
7. Turn your 360 back on, start Dead Rising and choose Continue Game. Outdoorsman will pop as soon as you're back in the game.
The save system has been updated adding more save slots so that could be the reason, either that or the whole Xbox system.