A Crossover Combination Finish is when 2 or 3 teammates jump on screen and do their Hyper combos together to KO an opponent.
Make sure you have at least 2 hyper meter stocks at all times, any time your opponent is low health, hit both Assist Buttons simultaneously and your team will jump out and perform 2/3 Hyper combos. You should see "Crossover Combination" pop up by the combo meter.
Save yourself time and hyper meter by setting the Arcade Mode to Easiest Difficulty and Damage to Highest.