Why did the Revolutionary Tribunal so powerful during the French Revolution?

You mean why WAS the revolutionary tribunal so powerful? Well, they had popular opinion on their side as well as a hundred percent belief that they were in the right. Jean-Paul Marat held sway in that court, examining whether a noble or sympathiser should be relieved of his property or his head.

It is often said that he was a psychopath or worse, but his identification with the struggle of the majority classes owning no property, few rights, his work for social equality made for a new invigorated France, a more moral one.

The power of the tribune was perhaps a sign to the popular mass that action was at last being taken against those who had oppressed them, de-enfranchised them for generations.