The most important element of winning DJ battles against the AI is nailing the freestyle sections and effects knob sections. Those count as percentage points, and whomever triggers them first gets 'em. Sometimes the AI cheats and gets them instantly, but usually if you keep an eye down the track and be ready you can take them.
The sections where you twist the knob are less essential, especially if you think you might miss notes to do them, but you should at least try most of them before the AI can.
Obviously, you still have to be proficient at your chosen difficulty, but using this trick I have won matches agains the AI that was outperforming me in a lot of parts.