Here's what you need to know.
First of all, you DON'T need to eat the pizza's. This unlocked for me without eating them. You do however, have to hit the pizza boxes. Unless you care about your leaderboard position I suggest ignoring them. You will most likely get 15,000 just by not being hit and by hitting every object. It is imporant to note that in the 3rd, 4th and 5th level there are shurikens and/or bombs in the pizza stages. In the first two there is not.
Second of all: I have listed many of the trouble spots in this game, but the big thing in this comes down to memorization. Shurikens, always come up at the same pre-determined spots. They vary VERY slightly in speed, and angle but for the most part come out just around the same way each time. Bombs also come out at a predetermined time. They always come out of the same spot, but the direction and speed of each one varies slightly. Pizzas and boxes come up in the same amount and numbers each time, but the angle and speed wildly changes from playthrough to playthrough (With the exception of the pizzas towards the end second level which always come in fours towards the screen). Pillars and wooden poles always come up in the same spot each time.
Also, you will get extra points for hitting dual pillars, or dual wooden poles at the same time. This is not neccessary, I got the achievement and accidentally hit a pair seperately.
Shurikens: You will hear a noise, and see a red blur, that lets you know these are coming. These will only hurt you if you get your body hit by them, your weapon can touch them. With the exception of early on in the second level (donatello) they always go diagonal. They mostly come from the top, but will occasionally come diagonally from the bottom. You'll need to duck out of the way. Be careful on the third level, on the first section with the two pillars, there will be a diagonal shuriken which will come down before you can even start taking them out. (comes from upper right) What I did was duck in the right corner and hit the pillar the second I saw them appear.
Bombs: A green blur will warn you about these. They look like green vials. These are tricky, you can't have your weapon touch them, but your body can. So feel free to move your legs around out of the way. If it's coming straight towards your weapons, you are allowed to stand still and as long as you don't see the color radiating out of your weapon it won't set off the bomb. Being a kinect game, the game might move your weapon slightly even when you aren't actually moving. Because of that I suggest moving out of the way the second you see a green blur. After it starts coming I don't suggest moving though. Unless you're playing the third level (Nun-chucks) in that case I highly suggest moving out of the way even if it is coming straight at you. Standing still will not help you as they jiggle around without your input. Also, the game WILL put you in unwinnable situations. Sometimes a bomb will come up, with a box going the same speed. In this case you can try to maneuver your way over to it, but more likely than not you're screwed.
The fourth level: I don't think any of the other levels really have anything tricky that I didn't explain in my bomb and shuriken paragraphs. However, when it comes to hitting every object, this one is a pain. There is three sections where boxes come down the left and right and you're supposed to hit them by throwing your Sai. The problem is, they start falling in horrible times. The first time is easy, at the start. The second time is during the exact time the first set of pillars come up. The final time is towards the end. After the second set of falling boxes you will have two wooden poles come out. After that two more wooden poles. The exact time the second set of wooden poles come out the boxes start falling. You can hit these by either throwing them or hitting them with your weapon. I personally choose to throw them as going from one end of the screen to the other can be tiresome or hard. It's your choice.