Every object includes the boards, stone blocks, wood/stone poles that appear and the pizza boxes. The bombs aren't included as objects you need to destroy and you DO NOT have to eat all of the pizzas that come out of the destroyed boxes.
If you pay attention to your surroundings and move your arms enough you'll be able to get this after a couple of goes. Memorize the patterns.
The levels I suggest watching out for most are Donatello and Raphael's levels since. Donatello's level has objects that fly from the bottom up very quickly at times so you have to hit it before it disappears off the top of the screen. Raphael's has objects falling on the outside of the screen that you're supposed to throw the Sai's at. Just stay focused and you should be able to notice them on the left and right.
Also know that you really can't lose this game, so even if you hit bombs and get hit by shuriken, you can still get this as long as you destroy every other object. This means you can swing your arms as wildly as you like to ensure that you hit everything. Good luck!