A competitive match consists of any Free For All playlist. Once you get into a Free For All match, change over to your knife. With the knife equipped you can now make your way around trying to earn your three kills with throwing knives/knife. Try to sneak up behind players so you catch them off guard as once you're spotted they will most likely kill you before you can react.
You can use the same method mentioned in "Call it a Comeback!" to get into the same game modes. Just get close enough to another play and either knife them, or use a throwing knife if you have found one through your multiplayer session.