Made a short video explaining how to complete this if anyone needed a visual guide. Completed it using 5 small cages with 2 Dogs and 3 mole rats, including using the Emitter to tame them.
Did all 5 at the same time and had no issues using this method. They remained tame long enough for the achievement before killing each other for whatever reason.
Also you will need 9 CHR for the perk to be able to make the Emitter.
"Wasteland Whisperer & Animal Friend" are required.
Total amount of resources required;
10 x Copper
30 x Steel
8 x Aluminum
4 x Crystals
5 x Nuclear Material
3 x Circuitry
2 x Rubber
Then for each cage, you'll need either ;
2 Brahmin meat, 4 Radroach meat, 2 Softshell mirelurk meat or 3 Canned dog food.
Confirmed it works with the rad roach and dog food.
Hope this helps guys!