EDIT: 04/24/23 I just received a message that the gazelles DO NOT count towards obtaining this achievement. Unfortunately I don't have the game anymore myself and can't check all the information mentioned in the comments in-game anymore. I deleted my original EDIT about gazelles being valid for this achievement based on the messages I received. Back in the day killing them worked for me, I just guess that they patched it. Happy hunting!
EDIT: 1/9/16 I just unlocked the achievement and I can confirm that it works with Newka-Cola and Nuka-Free. It isn't glitched either it is simply a huge pain in the butt. If you use any of the Nuka-mixes below you will have to face very short durations of the different effects on your character. You can push rb in the status screen of your pip boy to see if there is still an effect active. To give you an example: The Newka-Cola effect only lasted roughly 10 seconds. I could only kill around 2 enemies with one Newka-Cola. Feel free to use any of the mixes that you can create after picking up the various recipes in Nuka-World. Some of these will last much longer and will, therefore, make this achievement a lot more achievable . As mentioned in the comments, Nuka-Power seems to be the most effective mix because it has the longest duration of all the mixes.
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I want to point some things out, just to avoid confusion.
It is recommended that you do these kills before clearing all the different areas. It is easier to find enemies there than in the free areas around Nuka-World.
To get this achievement
you need to kill creatures that are unique to Nuka-World. Similar to the "kill x Far Harbor enemies" achievement of the previous DLC, just killing mirelurks won't do to net you this achievements.
Another very important thing to keep in mind is the fact that
you cannot just drink Nuka-Cola or any of its varieties like qunatum, dark, grape etc. You have to make sure to drink "Nuka-mixes". You can craft these via the new Nuka-mixer stations which are availiable in the crafting section in your settlements. If you don't want to build stations on your own you can find some of them in Nuka-World as well. Refer to the comments section to get details about their location in Nuka-World.
There are 4 different stations, but all of them create the same mixes so it doesn't matter which one you build.
Also, it doesn't matter which mix you drink. All of them are valid for this achievement. From the get-go you can choose between the following 6 mixes:
Newka-Cola (Nuka-Cherry + Nuka-Cola)
Nuka-Buzz ( 2 Nuka-Cola Wild)
Nuka-Fancy ( Nuka-Cherry + Nuka-Cola Wild)
Nuka-Free ( Dirty Water + Nuka-Cola)
Nuka-Love ( Nuka-Cherry + Nuka-Cola Quartz)
Nuka-Twin (Nuka-Cola + Nuka-Cola Wild)
Additionally you can use all the mixes you get for the various recipes in Nuka-Word. If you have already completed the main missions, you can still kill enough enemies in the surroundings of Nuka-World.
You should not have any problems finding enough materials to mix those, since Nuka-World is crammed with all sorts of Nuka-Colas. Keep checking all the Nuka-Cola vending machines and you should always have enough in your inventory to mix the hell out of that stuff. If you, nevertheless, run out of Nuka-Cola try the Colonial Taphouse in Diamond City. They usually sell them there. If they are out of stock just wait for 48 hours.
The video below shows all the new creatures that are valid for this achievement:
(Video credit: WackyWeirdo)
EDIT: As BLAZE VII pointed out: "I think rats and ants are easy to farm. Also no need to go do Diamond City, Shelbie Chase in the NUKA-TOWN MARKET always sells a decent set. Just sit next to the red chair and wait 48h but again."Hope this helps you guys!
Any improvements? Please let me know in the comments below!