Zeromus never attacked until Golbez and FuSoYa used Meteor on him, and until after Golbez tried to use the Crystal. Which is also why when you face Zeromus with your party, he does nothing until Cecil uses the Crystal and turns him into his second form. So here are the only two things that I think would trigger Zeromus to attack.

1. Casting Meteor. Golbez and FuSoYa both did this against Zeromus.
2. Attempting to use the Crystal and failing. Golbez did this, and Zeromus attacked shortly after.

I don't think any villain would use the Black Magic spell Meteor, or try to use the Crystal, so they would use their own special abilities, such as Giga Graviton, Light of Judgement, etc. Zeromus would null all the damage, but he wouldn't necessarily be able to deal any damage of his own. He would have to go into his second form in order to relentlessly attack. And in his second form, I think many villains would have a good chance of beating him.

But I think that Kefka might be able to beat him. Before anybody starts calling me a Kefka fanboy, I just want to explain why I think this way. The reason Cecil was able to use the Crystal was because and I quote from FFIV "the Holy power within" himself. I think it means Holy magic within Cecil, since he is a Paladin and Paladins are usually one of the most powerful types of warriors with Holy magic. Since FFVI says that Kefka absorbed all magic in the world from the Statues, he should theoretically have control over this Holy magic which is required to use the Crystal. Though this is just an educated guess, which is why I use the word "might" instead of "can."