To be honest, I don't know what kind of boss stage you could put in the game. I think its akin to something like Angry Birds. Levels became increasingly more difficult. A boss implies a physical force or some kind antagonist standing in the way of the of the player achieving their goal. A brick breaker game has a single purpose - to destroy the bricks. You could increase the health of the bricks. A boss might boil down to a brick that has to be hit many times, but I could see this mechanic becoming annoying. You could create something that fights back or deflects the ball or grabs it and throws it, but that would start veering outside of the brick breaker idea and start integrating other ideas. Of course, that is fine if that's your vision. I only wanted to point out various points behind the different schools of thought.
To me, and I want to stress this is only my opinion, all brick breaker games boils down to achieving the best possible score. So with that said, instead of a boss, what kind of mechanics could you create that would allow players to achieve varying scores each play through the stage and create an ability to top their own highest score each play through.