Every 5th level you get to in Revolution mode will be a "boss", and based on the item description you need to destroy the first one that you come to.
In order to do this you must destroy the red blocks within 'him'.
The easiest way is to keep some weapons as you collect them, rather than using them at the first opportunity. You can store up to four at any one time, so do this then use them and the boss will be gone within a few seconds.
Ideally you will secure a 'nuke', this is a flashing item drop which will have a wee rocket shooting upwards on it (the other kind is the 'smart bomb' which will be used instantly). When it goes into your inventory it will become a picture of a mushroom cloud. Keep this and use it as soon as the ball is in motion and you will have defeated the 'boss' for 10G and 10,000 points towards the high score achievements.