This was my final Achievement to obtain in this game. Initially I was frustrated b/c I thought there would be no way to obtain without having someone to locally play the co-op mode with. There were two issues holding me back.
One, I had no one locally to play with. This can be avoided by simply having another local profile log in. This way, you can start the local co-op game itself. Once the game has started, all you need to do is have that profile not continue once defeated and you can carry on normally as you one in a single player game.
Two, I was under the impression you're only allowed a certain number of 'continues' before you'd get GAME OVER. Just as x2i4eva above me has pointed out, you're allowed an infinite amount of continues.
Therefore, you can get this Achievement without breaking a sweat. I will point out contrary to x2i4eva's statement that you can state save (like in single player) in co-op mode (local or live) there is no Save file available.