This is where it all starts, this "Day 1" is actually only 12 hours long, from the time you land on the roof until midnight that night (give or take). Many of these survivors can be escorted together, but smaller groups are easier to keep alive and if you're moving fast enough there's no problems making a lot of trips..
After you land (the entire town flyover/photo sequence is skippable) and get into the mall, save, then head downstairs. Take pictures of all the survivors present to get the Portraiture achievement and start the Census Taker achievement (this is also your best time for the Group Photo achievement as well, go slightly up the stairs and snap a shot of the parking lot through the front doors), you'll trigger the cutscene by walking to the debris at the back of Entrance Plaza. Once you're in control again pick up the two baseball bats and bag of chips on the floor, then head for the stairs where Brad called you, fight what you have to but there is little point in drawing this out, you can't save anyone. Once the cutscenes in the security room are finished head for the ventilation shaft by Otis, he'll give you a map and radio before he lets you go outside.
Once outside, turn around and take a picture of the duct opening you just exited, if you're going for the PP Collector achievement you'll need this, but even if you're not it'll save you time and trouble down the road, trust me. Jump down and run to your right, toward the elevator, to meet your first survivor, Jeff Meyer, who'll ask about his wife before joining. Head to the left, stopping to pick up the baseball bat by the shelves, and around the corner, you'll see a doorway with Natalie Meyer, Jeff's wife, beside it. Approach her and call Jeff over, they'll run to each other and hug (have your camera ready to get the shot right as they hug and you should get both the Photojournalist and The Artiste achievements). Natalie will join after the hug ends and you talk to her, lead them both to the duct and you've finished the Survivor Escort Tutorial. Save and head back out.
Pick up the bat on the roof again (you'll go through a lot of them) and head to the door where you found Natalie to enter the warehouse. Drop off the shelves to the floor and you should get the Freefall achievement, then enter the hallway to trigger Jessie's cutscene; after you attempt to crush her skull with a fire extinguisher she'll ask you to help her partner, Brad, and give you a gun, just like any real life exchange. Exit the warehouse into the mall and pass through Entrance Plaza to the park, then proceed to the North Plaza, off to your right. Inside North Plaza head down the hall, taking the first right, and go down to the gun shop to pick up a sniper rifle (as long as you're here before 3PM you'll be fine, Cletus spawns after that). Leave and head back to the main hall, then continue to your right. At the far end you'll find a knife store, Ripper's Blades, drop what bats or other weapons you're carrying and stock up on as many swords as you can carry (I prefer katana's to the broadswords). Head to your right again, down the moving walkway, to Wonderland Plaza.
In Wonderland, go up the stairs to your right and enter the first store, Sir Book-a-Lot, where you'll find the Criminal Biography book at the back, this will extend the life of all your edged weapons (drop a sword if you have to, but I'm betting you'll have room by now). Leave the store and keep heading to your right, down the stairs and through the hall to the food court where you'll help Brad fight Carlito (this fight is only half the reason you grabbed a sniper rifle, so don't use all your ammo right now). After the fight, escort Brad through Al Fresca Plaza and into Entrance Plaza (through the most pointless cutscene ever) and talk to Dr. Barnaby, after which you'll be left alone with a final file in the case to fill; you'll need to go back to the security room to finish it, but no point going alone. Head upstairs and go into In The Closet, a clothing store with some zombies outside (only zombies on this level, can't miss it); go into the storeroom at the back and smash the boxes, to find Bill. Bill will says thanks and try to leave, then join you when he sees the zombies. Give him a pistol and head back to the security room.
Depending on the speed you're moving, you may be able to grab Burt and Aaron, possibly even Leah, inside Al Fresca Plaza while heading back, but if you're keeping a fast pace there's no need to wait for them to spawn.
Escort Bill through Al Fresca, the Food Court, Leisure Park, and into Paradise Plaza, go up to the coffee shop and talk to Kent. Kent will teach you about taking pictures, get one of him doing his pose that scores 500 PP (Make sure Kent is centered and zoomed in so that he's in the frame and snap a photo as soon as he crouches to take a photo of Frank ), then another one for 700 PP (Wait for Kent to snap a photo, he'll pump his fist right afterward, shoot a picture just as he pumps his fist ) and you're done. Take Bill through the warehouse, up the elevator, and into the security room to trigger the cutscene and finish the first case.
Head back to Al Fresca Plaza and smash the boards in front of the clothing store, Weber's Garments to find Burt and Aaron. You'll need beat up Burt a little bit before he'll join, at which point Aaron will join as well. Escort them back to the security room. Again, depending on the speed your moving, and how long you had to work to get Kent's pictures you may be able to pick up Leah here as well, but if you're still moving fast enough she won't spawn for another couple hours.
When you head out again things'll get a little interesting as the convicts will have spawned by now. You'll need to help Sophie, which you do by watching the convicts murder her boyfriend (he can't be saved) then chasing her through Leisure Park until you get her attention, at which point she'll join and you can escort her back to the security room. After Sophie is safe head back to Al Fresca, dodging the convicts in the park, as Leah will have spawned in Riverfield Jewelry now; Leah will take some convincing and arguing but will join, however you'll need to carry her due to her injury. I'd recommend a save before leaving Al Fresca (there's a washroom in the back of Flexin, the gym by the food court entrance) as this can get hairy. The convicts mostly hang out by the food court entrance, mostly, so they'll jump you as soon as you go outside, but they're not very good at what they do. Pick up Leah and run through the fountain or past one of the benches and make for the trees, odds are they'll get hung up someplace, leaving you free to take Leah to the security room. Once there, grab the coffee creamers by Jessie and save, as shit is about to get real.
Head down to the park and climb up on top of the covered picnic area (you can jump up at the corners and grab the ledge to climb up on top) then look for the convicts, they're likely hung up over by the food court someplace. Get your sniper rifle and use it to shoot all 3; kill the one on the gun first, then the driver, the passenger will move to the driver seat, so shoot him as well (Note: This is best case scenario, they can get hung up someplace where you can't hit them and you need to get a better angle from the ground). You don't need the Jeep for this next step, but as climbing into the Jeep's driver seat will give you the Carjacker achievement anyway, this is a good time to head down to the underground maintenance tunnels (through the alleyway at the northern end of Leisure Park). Once in the tunnels make a right turn, then at the first intersection take a left, then immediately take another right, and you're at the warehouse; inside, at the back, you'll see the Maintenance Tunnel Key floating, grab it (there is also a sub-machine gun near some barrels if you're inclined) and drive back out of the tunnels, over to the North Plaza entrance; when you get there get out and 'Examine' the gun on the back, this will allow you to pick it up and carry it (Note: the gun cannot be stored in inventory and only has 200 rounds so be careful with it, don't drop it while exiting areas, it won't respawn).
Once in the North Plaza head to the gun store, Cletus will have spawned and will shoot a survivor when you show up, (he can't be saved, so don't sweat it). If you're going for the Psycho Photo and Psycho Collector achievements this is where you need to start (grab a photo of Cletus as he's drinking for maximum PP). Cletus is a tough fight, I've found the best way to handle it is to be aggressive, as soon as you have control start shooting, you should be able to hit him a few times before he hits you, which will make you drop your gun. You might be able to get some cover behind the displays, but it's spotty and his shotgun blasts will hurt, so try and blast him down fast; if you do get some cover, he will shoot 6 rounds before having to reload, if he hits you he'll celebrate with a drink, giving you time to recover. Once he's dead (this will give you the Self Defense Achievement) take your gun and head out toward the knife shop, be careful as zombies will be thick now (I like to use the back hall shortcut to save time and trouble); there is a washroom halfway to the Rippers so if you've gotten this far, for the love of god, save. Run into Rippers and grab as many swords as you can carry, you won't need them much longer, but they'll help you keep that gun. Head to Wonderland for the next and most important psycho fight of the game.
Inside Wonderland Plaza head to the bookstore where you got the Criminal Biography book, Japanese tourists Shinji and Yuu will be waiting. Pickup the Japanese phrasebook on the floor by the till so you can talk to them (you'll need to keep it in your inventory for the entire escort) and ask them to come along, they'll talk to each other for a bit before eventually agreeing to join when prompted a second time. Once they're on-board give them some weapons, like those swords you're carrying, and head over to the Space Rider machine to meet Adam the Clown.
If you're not prepared for this fight Adam will take you apart, even being ready he can be a lot of trouble, and after fighting Cletus you won't have a lot of ammo left. Adam can block the bullets with his chainsaws, so don't burn them up, keep your distance and wait until he starts to inflate a balloon, then shoot it, this will both damage him and stun him long enough that you should be able to finish him up. Once his death cutscene is over drop the gun and grab his chainsaw, you'll never need to look for another weapon.
With chainsaw in hand examine the control panel, the ride will stop and let Greg off, he'll join as soon as you talk to him and offer to show you a shortcut to Paradise Plaza. Grab a second chainsaw (never hurts to have a spare), make sure your tourist friends are still tagging along, then follow Greg (don't lead, he needs to show you the way) to the washroom on the lower level. Give the game another save, jump to Paradise Plaza, and run these guys up to the security room. You can now drop the Japanese book and forget about it.
After saving, head down to Bachman Books, by the washrooms in Paradise Plaza (under Colombian Roastmasters), and grab two more books, Engineering and Entertainment ; between the 3 books you're now carrying the chainsaws will be good for roughly 2700 (two thousand and seven hundred) kills each, saving mucho time looking for weapons and maximizing your efficiency. Head over to the North Plaza to look for David Bailey, he's in an empty store about halfway down to Rippers, on your left hand side. David will take a little convincing, but will come along with assistance; he'll need your shoulder to walk, but at least you can keep him close and the added bulk makes it easy to push through crowds. Once he's in the security room you should have a couple hours to kill before the next case, so save up and go find some trouble.
This is a good time to wrap up some achievements, like Raining Zombies, Costume Party, Strike (Pro tip: take a bowling ball outside and throw it through a zombie cluster at one of the entrances), Sharp Dresser, Zombie Road (maintenance tunnels is best place for this one), and get working on Karate Champ.