Wasteland 3

You can do this everywhere using a shotgun but the best place to do this is in "Dontown Colorado Springs" (The 3rd area you enter in the game, right after leaving "Ranger HQ") at the very begining of the area you see a group of Dorsey prisoners wating for execution, equip a shotgun with one of your characters and use "Attack Mode" button (Y button) to kill at least 4 of them using one shot, the achievement will pop up shortly. Also feel free if you want to get the other achievements like "Badda Bing" (blew up 6 enemies using a single explosive attack) with these poor prisoners.

While a lot of methods work, most of them can be missed if you continue the story. However, after completing Denver you may notice the section to the right when you enter the area has tons of mutants. I'm thinking over 50 and they're all close together. Most likely you ignored this area and didn't attack them. I was easily able to kill 6 or 7 with one shotgun blast at level 23.

For best results, I had small arms maxed, used the Devastation perk (gain 25% damage for each enemy hit with same shot), put points into Weird Science (probably not needed), and used the Cold Comfort shotgun which does 30% damage to mutants.

I saved before attempting, and ran my character into the middle and used the strike attack option. I just used Lucia Wesson.

If you need the rocket launcher achievement for hitting 6 enemies, it's also very easy here.

This is fairly simpel. Just go into downtown Colorado springs with a shotgun equipped, find a group of four civilians close to each other, quicksave, aim manually so you have all in your cone, and fire.