Hey, I won this twice with a gamepad, once was on a full blown melee character. Pick an automatic pistol (like Lexington), shoot all targets multiple times (not only in your lane) and you should be fine. No perks will help you here anyway (except faster reloading). Might wanna practice targeting in an uncrowded area somewhere, but the contest is not even skill-based.
To be honest, the reward isn't worth the hassle.