There isn't a definitive way of completing zombie genocide master as of now, but the most likely way you're supposed to do that achievement, using the SUV, should be handled with care before any brave soul dares spend six hours running over zombies, only to find out the military arrives and the game ends with the player only having a 68,000 zombie kill count. Here's a few calculations to decide whether this method is for you. NOTE: I have not gotten the achievement yet, only 4 people have, and I'm not spending the time to get it unless I know it's a feasible route.
 
For all given purposed you have 72 in game hours to complete the achievement, kill 72,000 zombies before the military comes. that means that you have 1 hour in game to kill 1000 zombies. Each in game minute is 5 real life seconds. So 5*60 = 300 real life seconds/60 = 5 real life minutes to every 1 in game hour. I did a quick test running down zombies with the SUV, and it took me somewhere between 4 and 5 minutes to kill 1000 zombies. Mind you, the Day 2 rock concert was going on, and that horde of zombies is fairly large, so my estimate may be inflated, or it might be accurate. 
 
What matters is that you need to kill 1000 zombies every 5 minutes that you play for the entire 72 in game hours. Now, there are other things you have to take into account becuase they take time to get. Most emphatically, the Driver magazine and the SUV dieing after a certain number of zombie kills. Can you still get 72000 kills after getting the magazine, and walking to a gateway, returning and beginning to drive again for every iteration of the car breaking? This estimation of time taken is unknown, and where the car "dies" as to the location of a gateway into another casino zone is very important, and the zone matters since you need to walk to the top of the silver strip to pick up the SUV and begin the slaughter all over again.
 
Those are the variables with the SUV method. It's up to you to decide whether or not you do this method or something else. If the people who got the achievement chime in on how they did it that would be good as well. Good luck to everyone who's dumb enough to spend 6 hours on this achievement, which i am included in.
 
EDIT: I'm sitting at 10,207 zombies at 4pm day 1, and am seriously considering just not doing it anymore because I'm so bored. It is 4 AM though...

I know that with time people will get it. Right now it is just a matter of someone finding a fairly sure way of doing so. I would not mind being one of the first people to get it, but I don't see it happening. I know I am going to try for it. It was hard enough getting the blaster in DR1. But that had a reason to get it. There aren't any perks to spending such a great amount of time on this trophy. Just how it is. I would love to hear from some people that have completed it though.  

You have more than 72 hours. The game starts 4 hours before the 72 hour countdown that's supposed to be used to get Katey Zombrex. This is more than enough time to get the magazine and the SUV and get some kills in before the 72 hours. Some tips I read from a developed meathod were just to keep moving, don't bother ramming against the groups that gather by walls because it slows you down and you only get credit for kills from the ones you directly hit. The rest are just getting knocked down by other zombies. Also, don't leave the area. To respawn zombies stop by the save point in the middle, save, return to the menu and reload. Then take the mall car and drive back to the SUV and repeat.
 
@marioncobretti said:

" Theres a glitch with co-op magazines that will let you have 10 bike magazines in your inventory (similar to the egg glitch in resident evil 5) it will guarantee the full 72000 odd as the bike is almost completely invincible, ive read youll only need 4 of them to get it. "

I really wish I had found this before I started my attempt. The maximum I killed was 68k before it ended. I have a saved file with 62k zombie killes and 5 in game hours remaining, please tell me theres a way for me to get it without starting again. I have to say the reason I was going for it was for the unlock and it's just come to my attention that there is no fucking unlock, FANTASTIC!.

I'm sure this has been stated before, but I'm almost 100% sure that your actual Attack stat figures into the effectiveness of the vehicle as well so it would probably be wise to wait until you've maxed it out. Even if that isn't the case, having a hire natural speed stat certainly wouldn't hurt either. 
 
I'm also worried about accidentally triggering Meet the Contestants while doing this though I may take a stab at it this weekend anyway.

" I'm sure this has been stated before, but I'm almost 100% sure that your actual Attack stat figures into the effectiveness of the vehicle as well so it would probably be wise to wait until you've maxed it out. Even if that isn't the case, having a hire natural speed stat certainly wouldn't hurt either.  I'm also worried about accidentally triggering Meet the Contestants while doing this though I may take a stab at it this weekend anyway. "

So far I'm on target at 34,000 kills, but I'm struggling to make the 1000kills per hour, it's more like 900 so I'm slowly falling behind and it could end up costing me at the end. It's pretty much 6hours of constant driving the SUV and that thing does not handle well, several times it has got stuck on a bench or rail which has forced me to reload. Honestly I don't know why I'm even bothering but here's a good guide for those wanting to do it, there seems to be alot of people failing on 70,000kills which must really suck...
 
 http://www.xbox360achievements.org/forum/showpost.php?p=3558889&postcount=107
 
I've been saving every 1500kills so perhaps that's where I'm slowly failing, too much time spent in the buggy driving to the SUV from the save point. Anyway, off to download more podcasts to help me through it.

THERE'S A GUARANTEED WAY THAT I FOUND AND I MADE A SHORT GUIDE FOR IT, I POSTED IT ON GAMESPOT, heres the link  http://www.gamespot.com/pages/forums/show_msgs.php?topic_id=27477012

I just want to say that I AM THE ZOMBIE GENOCIDE MASTER!!!!!!!!!!!!!!!!!!!        I did this WITHOUT doing case files and Failed all cases and didn't give katey zombrex.
Now I do have this game on pc as well and have all but 3 trophies on that platform including this TROPHY.  This is one of the hardest trophies to obtain by far, not because its 72,000 Zombies to kill  but because your under that ever decreasing time limit. Through out my FIRST iteration on ps3 I was doubting myself by the second day " damn i can't get it i need 30,000 still man blah blah."  I wanted to know if you could even complete this without doing cases and such.
i found this.......
9/25 0300 start time
9/25 grab driving mag 
9/25 0334 arrive at HMMWV (SUV)
and this is where i slaughtered the Zombies
9/25 0700 - you need  2,750+ kills   (my kill count 5,006)
9/25 0800 - katey turns and all cases fail
9/25 1900 - 10,000 kills   ( 16.450)  this is the first cut-scene where it is night time and the Zombie's become more frivorlous you can see I am making the 1000 an hour and then not making 1000 an hour
9/26 0700 -  22,000 kills    ( 25,890) 
9/26 1900 - 34,000 kills     (38,003)
9/27 0700 - 46,000 kills     ( 51,230) 
9/27 0813 - (53,596 trophy boop booped)
9/27 1900 - 58,000 kills     ( 63,760) 
9/28 0634 - 72,054 kills trophy boop booped
9/28 0700 - you need to have 70,000 + kills  cause 1000 on 9/28 military arrives dubbing you the reason they callit the GREENE OUTBREAK  
this was one of the most redundant, boring and tedious trophies to get. 
9/28 1000 military arrives  and my kill count then is only 73,458 cause i let popsicleman89 co-op when he buzzed me
so as you can see this trophy is do-able just do nothing but drive up and down both strips and the arena.... REMEMBER IT TOOK ME A MIN. TO GET THIS..... DON'T BACK UP OR DON'T DO THREE POINT TURNS AND AVOID WRECKING IN CORNERS ETC.  IT'S INEVITABLE THAT A ZOMBIE OR TWO WILL GET STUCK UNDER THE HMMWV AND THE DAMN WHEELCHAIR AND THE WHEELED CART THING, JUST DRIVE LIKE YOUR IN NASCAR AND KEEP THE MOMENTUM UP ECH HMMWV CAN LAST ANYWHERE FROM 2,000 - 4,000 KILLS PENDING ON IF YOU HIT CORNERS WALLS ETC.  HOPE  THIS  WORKS  OUT  FOR  YOU : )