How to Survive: Storm Warning Edition

i get this on los riscos island at the bottom of the map at the campfire

I got this one first try on Challenge 3, the same one best used for cracking out and all the stackables that go with it.

For this achievement I only needed to set it to Normal difficulty (I didn't try Easy so not sure if enough zombies will spawn). Once you wake up exit the spawn and grab your weapon of choice and some ammo, run up to the top of the map and round the back of the spawn shack to grab some fresh meat.

By the time I'd got the meat and continued running round and was back at the door of the spawn there were quite a few zombies milling about. After kiting them a little while longer I ended up with two boomers as well, once they're there and there looks to be at least 20 zombies, chuck down the meat. I then ran round to the back of the group (as the boomers walk slower) and once they were all fairly close killed the first boomer and switched to the second boomer, with both these explosions you should wipe out the group of 20+, do keep shooting though to finish off any stragglers, just in case.

I got this on Santa Barbara Island.

When you reach the first safe zone (the camp where you can sleep), run inside and close the gate. Kill the zombies inside until they stop spawning. All the zombies outside will pile up outside the gate, including 2-3 of the exploders. Just open the gate and open fire... try to target the exploders first and pick off the extras quickly. Personally I used a crafted machine gun which got the job done nicely. Any powerful weapon or explosive will also work.

If you don't already have it, this will also unlock

*My method is quite similar to what Dark2099 already says above but I found kinda glitch to make this really easy for everyone*

When you reach Santa Barbara Island you need to get to the first Safe Room where you can sleep and save. Make sure you collect the can right in front of the safe room unless you do already have 2 of them. Also smash these two wooden boards left and right of the safe room to collect fuel and one part to create a weapon. In my case I was able to build a "Strong Chainsaw" then which requires all 3 parts i've just mentioned to build.
Open the Safe Room and close it again immediately. Many zombies will run towards the entrance but won't do anything. The only thing you have to do now is to fight the zombies spawning inside the Safe Room. As they are armed and plentiful take the chainsaw and cut them into pieces. Be aware that the collected fuel will not last for ever. It is often enough to touch the zombies for a short period of time with the chainsaw to kill them.
Once you've killed all the zombies inside take a bow (I used the strong one which makes more damage; you should have already created one in one of the previous Islands) and keep shooting through the closed door. Try to hit the small holes in the door. Keep doing it and you will start hitting zombies although the door is closed!
In my case I hit a "Boomer" through the closed door which made him explode (all other zombies were dead too) and the game seemed to pause for a second then I found myself back on the XBox Dashboard and the achievement popped for me.

I found this "glitch" accidently but it worked for me.

Hope this helps!