Sadly, these are a bit more annoying than super arts and Pandora activation. It will require you to equip whatever gem units you can to boost your cross meter, ideally by landing special moves if you can. Either way, the character you'll be using is Yoshimitsu. The move you'll be using is half-circle backwards + punch. This is the best meter bolstering move in the game and you'll need to do it for both Cross Assaults and Cross Arts.
Cross Arts are executed using a quarter circle forward + Medium kick and punch. It should grab the opponent and combine the two super arts of the characters, doing some major damage to your foe. When you're doing this, you'll want to lower your foes to a sliver of health so the initial impact K.O's them rather than having to watch the full animation. This saves off quite a few seconds, saving you some serious time in the long run.