A Crossover Combination is performed when you have 3 or more Hyper Combo Gauge Bars, and hit Both assist buttons at the same time (LB+RB). All your characters will come out and use an Ultra all at once, so you need to have atleast 2 characters alive to do this. If you kill an opponents LAST character with this, it will count as a Crossover Combination Finish. This is easier to do if you active X factor first.
NOTE: The game is finicky about Awarding CCF's, if only one character is attacking when you kill them, it WILL NOT count (Meaning, your other characters finished their attacks and already hopped off screen)