To do this, you must have the Acid Bath weapon part. This part is found in Chapter 11 in the optional quest "Armory". You must get to the end and open the container with the rewards. Attach this to your weapon at a workbench. When you shoot enemies, they will start burning from acid. You can get this over time throughout your playthrough. If you want to get it all done at once, you can play the Co-Op mission in Chapter 14 while playing as Carver. At the final nightmare you will get to the end where you have to destroy the symbol in front of you. Instead, stay next to it and shoot the frail feeder shadows. Move forward to respawn some. They will sometimes stop running at you when in certain spots around the symbol making it pretty easy to maintain your kills. Just be warned, that in Co-Op play, your stats will often reset if you die or quit out.
You will most likely need to use a higher level of acid bath. I tried to use a contact beam with level 1 acid bath, but they wouldn't dissolve. Just get to your second playthrough and get the MK-II acid bath, it will work better.
Just create a gun with acid damage and kill 50 necros. Confirmed the necros only need too die from acid damage and do not need to be completely dismembered. You'll see a green splash when acid damage is used on them correctly.
Equip any gun with Acid Bath and just shoot you will get this I promise this was my first "Kill such and such with such and such" achievement because it was the first one I went for thinking it was going to take forever I got it in no time before I even launched to Tau Volantis
I've found that equipping the acid bath to a ripper blade with it's default head is a great way to get this achievement due to the way in which the blade damages the enemies. Also a great area to get this is the Armory since there are a lot of feeders which are easily farmed by a ripper blade
Netween using Ripper Blade for this and doing Electric Lawnmower (using electric charge instead of acid bath), you also end up getting Empty Chamber as well (it counts as a melee Weapon Part it seems) And the Armory is definitely a good call for farming up the kills