Killer Instinct

Select practice mode choose Kilgore, opponent does not matter, I used Thunder. Once in practice mode hit the menu button, press RB twice to get to the practice options menu, set your instinct meter to Infinite, press B to get back to your practice battle. Once here activate your instinct and then do any of your chaingun attacks until the achievement pops, I used half circle forward with the right bumper and kept hitting it over and over until i got it.

I just discovered you can earn this without buying Kilgore.
I got this achievement on accident without buying him.
I went to Trials which is under Single Player, then Master. I had a trial to "deal 20% damage as Kilgore in practice mode". I clicked it and it took me in to the practice mode versus Riptor. After playing around with him for a bit I put on infinite Instinct and let loose with the gatling guns. Next thing I knew I popped the achievement!
Sadly I can't get any more of his achievements until I buy him.

Easiest way besides buying straight out is to play "Shadow Lords" and finding a multi part Ultratech mission where you fight him a couple of times. After that, you can add him onto your team in place of another fighter. When you do, activate the Instinct mode and use any Chain Gun special.