We don't use "fighting" in English to encourage people. If you said that, I'd think you were reporting a brawl. "Come on!" or "Let's go!" or You can do it!" are all fine for encouragement.

I'm afraid that that is more of a cultural question than a language question. 'Fighting' would probably be too aggressive in a western culture. 'Come on' is possibly a little colloquial, but I thought that you were asking about a slogan. Slogans are not necessarily formal (in western culture at least). Maybe you could ask the class to find a suitable slogan? They might find something from popular culture that resonates with them? From a popular movie or TV program perhaps?

"Fighting, Class 2" sounds weird. A note about "come on", I see a lot of non-natives use this from all over the place, and from all different types of language, and I've yet to see it used correctly. "Come on" as a cheer, has to be like, a shout, really loud and emphatic, and thus is only really appropriate if... I don't know, you're watching a sports game and yelling at the t.v., or ... maybe you're in the gym shouting and encouraging your workout partner. When a person uses "come on" in any other way, especially in writing, it sounds VERY sarcastic, and often seems to express annoyance, which it almost never what non-natives indeed to use it for. So, yes, you could use "come on," but you have to like, shout it, with a fist raised in the air, or else it doesn't come off right.

Do you mean you want to say something like 加油?