Here's a quick walkthrough, starting with a new game:
1) Setup
Head to the pharmacy, rescue the pharmacist and get Zombrex for Katey. Entertain yourself until the pawn shop mission unlocks (you might have to give Katey Zombrex at 7 for this to occur). Run out to the strip and talk to the hoodlum to unlock all the pawn shops.
2) Royal Flush Plaza
Head back into Royal Flush Plaza and make 2 laps of the mall, 1 per level. Don't forget the kiosks in the center - there are some on both floors.
3) Slot Ranch Casino
Head over to the Slot Ranch Casino near the pharmacy. Run through the casino to the food court and do a lap, entering all the restaurants. You might want to grab some steak from the BBQ place in case you take damage in the next area.
4) Yucatan casino
Run into the Yucatan casino. After the cutscene, run into the restaurant to the north. If you are reasonably leveled up, the psychopath won't hurt you much and the kitty will likely get hung up on zombies and slot machines. I also entered the dance club to the east, but I don't think that counts as a "store". Exit into Palisades Mall to the southeast.
5) Palisades Mall
Make a lap of the lower level of the mall, then head up the escalator to the second floor and make a lap of that. Don't forget the small kiosk on the second level (at the pawn shop end). I also entered the grotto bar, just to be on the safe side. Exit via the Atlantic Casino to the southwest.
6) Atlantica Casino
Run through the casino, hitting the coffee bar on the way. Exit to the strip.
7) Silver Strip
Head northeast on the Silver Strip, hitting the stores on the south side until you get to the restaurant outside of the Yucatan. Make sure you hit the kiosks in the center (Juggz Bar & Grill probably won't identify itself - just jump inside to be sure it registers). Now head back down stores on the north side of the strip until you pass the central park and enter the Platinum Strip. Don't worry about doors you can't enter, like the wedding chapel and the peep show.
8) Platinum Strip
The Platinum Strip has a set of six stores about halfway down so hit those and then proceed to the far end by the arena. Go past the two souvenir kiosks (I think they count as stores) and head inside the arena.
9) Arena
Hit the two souvenir stores at the back. Lots of zombies here but you can sneak past on the sides pretty easily. Exit from where you came in unless the Americana door is open from a prior case.
10) Americana Casino
Head into the casino and enter the bar in the center and the restaurant at the back.
That's it - achievement unlocked.
Some tips:
* You can do this over multiple playthroughs (confirmed by a buddy). I did a dedicated run, though, just to be sure I hit everything. All told, it took maybe an hour which wasn't too painful.
* You won't need much in the way of weaponry if this is a dedicated run. Just make a spiked bat or two on your way out of the safe room. Occasionally you will need to clear out a bunch of zombies in front of an exit door and the bat will do this with one swing. Jump kicks will also clear a path if you are unarmed.
* You'll take some damage from random zombies and in the Yucatan so carry some OJ or meat for healing.
* I made sure that the name of the store appeared in the lower left of the screen as I entered them whenever possible. There was a kiosk on the Silver Strip that didn't "identify itself" for me (Juggz Bar & Grill). It's probably best to get all the way into the store and linger a bit just to make sure the game registers it.
* There's no need to worry about the case files, survivors or Katey, though you do need to rescue the pharmacist and (possibly) give Katey the first Zombrex to unlock the pawn shops.
* As far as I can tell, you don't need to worry about rooms that are "non-store-like" or with closed doors. I hit as much as possible, though, just to be on the safe side.
* I think you might need to hit the pawn shops. I don't think I went in all of them before I did my run, but the achievement unlocked for my buddy when he entered a pawn shop with me. I've updated the guide to include unlocking the pawn shops at the beginning.
* The in-game map is really good and I popped it open frequently to plan my route. I didn't bother to print out a map and tick off stores since it's pretty easy to keep track of where you've been. Just make sure to take special note of the first store you enter in an area so you know when your lap is finished.
* You definitely do not need to enter the hotel off the strip or the construction area.