EDIT: As of 18 June 2020, it looks like this has been hotfixed and just requires the kills now. To make sure your hotfixes are applied, wait at the main menu for a minute after starting the game. A sign will appear on a telephone pole behind your character letting you know that "Hotfixes Applied." Until this hotfix is actually patched into the game, this the way to get this one.
THIS ACHIEVEMENT IS BUGGED
I've opened a ticket with 2k and Gearbox, so hopefully they take care of this pretty quick. I've killed all 4 multiple times and have not been able to get more than 50% on the achievement tracker.
It appears that this achievement is not bugged, just unclear on what the actual requirements are. The way to get progress on this achievement is to have the rare spawn "Kill" missions, which can be grabbed on the second story at the Lodge.
"Kill" missions are supposed to show up for you when someone on your friends list kills the rare spawn. This does not appear to be guaranteed. If you need someone to kill the rare spawns multiple times, feel free to add me and shoot me a message.
To help people get this, I have made a channel in my personal discord for this achievement. If you're looking for people to add, discord.gg/7beg6Kw and there's a channel for this achievement. If there's a better way to coordinate people outside of discord, let me know so I can get that up and running.
If someone on your friends list has the missions, you can join their game, kill the enemy in co-op and you both get progress for the achievement. Thanks to Stumpadiah, ☽Somaloria☾ and Sighris for testing this in the discord.
Huge shoutout to Swan in the discord for finding this out: After adding someone on your friends list, have the person who needs the missions go to the lodge in a new session(save/quit and reload the game) while the other person kills the rare spawns. This seems to give the person in the lodge the missions each time.
There are 4 rare spawns and I've included a map with each ones locations below. CURSEHAVEN
For this one, the Lantern's Hook fast travel is the one at the bottom of the screenshot.The Cankerwood
Fungal Gorger - NEGUL NESHAI
Shiverous the Unscathed -
Voltborn - QUEST LOCATIONS