How do I do a plasma explosion particle effect?

Is it possible to do complex particle effects in C2 like fireballs and plasma explosions or should I use a third party software?

Yes, you can do it in C2.

But that is a fairly advanced topic on the art side of things. If you have no idea how to go about creating the art yourself, a third party generator may be better.

After all, there are hundreds of different ways stylistically to render a fireball or explosion.

do you know what are the best software to do that?

Best is subjective... but Adobe Aftereffects is a fairly well known one. There are probably others more suitable for what you are trying to do. Depending on what you're trying to do.