Start as Mamluks, attack Ethiopia and one of its two neighbours bordering you: you'll need to have a land border to the two Jewish provinces Semien and Dembiya (look up Beta Israel) that you need to take. Once you've taken them, core them and beat the separatists rebels. We don't want them.
After that send a missionary to either of the two provinces to convert them to Sunni, while also setting the missionary maintenance to 0, so that it actually never gets converted - all we want is to be converting them for as long as it takes to spawn Jewish Zealots. And it may take a couple of years, or even more. You can go to another war to get all the other remaining provinces that are needed for the achievement, that aren't under your control yet.
These zealot rebels, once spawned, will go around your territory and convert every province they occupy. Ideally, you want them to occupy as many of your provinces as possible before they enforce their demands. What helps is to run after them and de-occupy provinces to slow down the "enforcement" progress, to give them more time and more provinces to convert. Otherwise we will have to convert the remaining sunni provinces ourselves. We'll have to do it either way, the only question is how many.
Once the demands are enforced and state religion is changed to jewish, you want to bring back the missionary maintenance to the maximum and make conversion autonomous. At this point you will be able to open your first idea group and it should be none other than religious ideas, to get more missionaries and the missionary strength modifier.
With that, just wait for the conversion to finish, while also applying various bonuses for the missionary strength: check decisions, jewish religious aspects (also select the required Jewish Community aspect), unlock ideas, check if a corresponding administrative advisor is available etc.
As a Jewish nation, convert all of Egypt to Jewish while having the Jewish Community Aspect active.
