PROTOTYPE

A rather easy trophy, you just need to put in the time to acquire enough EP to purchase all of the upgrades. You will easy have enough long before you finish all the extra side missions such as collectibles and events. So just keep chugging along and this will be yours in time. However, if you are impatient and need this ASAP, this strategy discovered by osakamitsu on our sister site for easy EP during the "Biological Imperative" mission should be highly effective:

"You can most likely do it with any helicopter, but I am about half way through the game and I am on a mission where I have to jack this helicopter and it has like 160 missiles or something and a machine gun. You are told to go fly over the infected area and scan the infected water towers for a suitable enemy type. Well instead of doing that fly to the infected area and start shooting the infected water towers that are around all infected the areas. You get like 8,000 EP for each. Shoot 25 of them and you get the achievement for killing the infected water towers without them hatching. As long as you properly hijack the helicopter and no one suspects you as a bad guy then no one attacks you while this is going on. 1 water tower takes 1 missile. 1 fly through with this helicopter can net you 1,192,000 EXP assuming you find a water tower per missile! And even more than that if you use your machine gun. I am buying upgrades left and right! ones that cost like 273,000 EXP are mine in no time. I usually go until I have about 500,000 EXP or so and crash the heli and do it all over again. Hope this helps!"
I can also confirm that this works just as well outside of that mission. The only difference is that you'll need to find another helicopter by yourself when you run out of ammunition. On the plus side, shortly after that mission you will unlock the Infected Vision ability, which makes the infected water towers much easier to spot.

Thanks to JK_Blade for pointing out that I forgot a major detail regarding this trophy: Not all of the upgrades required for this trophy can be purchased in the manner described above. You will also need to infiltrate the military bases and consume marked military personnel to acquire some of the upgrades needed to unlock this trophy.