Have you visited.
www.axololt.org
Also, link for cycling:
http://www.caudata.org/cc/articles/cyclingEDK.shtml
Cycling is establishing good bacteria to cope with things like ammonia and nitrite; but first it has to establish. Basically, from the day you put your axies in the tank, started feeding them is when you started cycling the tank.
If ammonia and nitrite levels are too high they are controlled through regular (daily if necessary) waterchanges of about 20-30% of your tankwater.
Anyway, since your good bacteria isn't established yet, you have to monitor the water quality, ie use Freshwater test kits for ammonia, nitrite and nitrate, every day or two days (probably daily during this heat), and do daily/every two days 20-30% waterchanges to keep the levels from being too toxic (safe enuf for your axies to live in).
4 days - which means you should do a waterchange today/tonight to be on safe side (only 20-30% not complete waterchange); and if you don't have test kits for the 3 mentioned, then take a sample of water to your petshop and get them to test and give you the results. Meanwhile don't add any chemicals (ie to "fix ammonia levels") and do daily 20-30% waterchanges .
Regarding filter, do you have a hang over the back one, if you can adjust the water flow so it isn't as fast would be good. And also, tie something either around the water outlet flowing into tank, or put something beneath it so the flow hits it and is cut down a bit. No need to clean your filter.
How long is your tank cm/mm or inch measurement and were all the axies in the one tank when the others died?
How large are your axies and how often do you feed them? When feeding try not to stuff them too much, axies will tend to overeat if they're given the chance. As they're eating till they get sick then cut back how much you feed them. If you find any uneaten/regurgitated food in the tank try and remove it within an hour of feeding, otherwise it adds more waste to the tank.
Invest in a turkey baster, they are handy for picking up uneaten/regurgitated food and axie poo (when you find them before they disintegrate) and once your tank is cycled (takes several weeks).
What is your tank temperature - try and keep the tank below 24 degrees, which is stressful for axies, ideally below 20 degrees would be better. Use fan blowing across the surface to cool it down or frozen bottles of dechlorinated water (water treated with a dechlorinator/water ager/water conditioner to remove chlorine and chloramines) rotated (before one completely melts swap it for another frozen bottle). Don't use icecubes as it will cause fluctuating temperatures.