They may call it acting for a reason, but there isn't all that action in this play. Let's face it: there's not much you can do when the main character spends almost the entire duration chained to a rock in the Scythian wilderness, only to plunge into a bottomless pit at the play's ending. Or, you'd think so, anyway.
The thing is, even if Hephaestus chained Prometheus's body, he didn't chain his mind or his tongue. Putting those two assets to use lets Prometheus unleash an unrelenting flow of insults and defiance against Zeus. He also reveals his confident belief that Zeus will one day be dethroned by a descendent of Io. In a way, you could say that Prometheus's speech reveals more about his defiant character than any actions could. Like this:
I tell you that even though my limbs are held
in these strong, degrading fetters,
the president of the immortals will yet have need of me (168-70)
Get it? He's hot-headed and self-assured: this doesn't some like someone who's going to be giving up any time soon.
We also learn a lot about characters from what they say about themselves or about each other. The problem is that this kind of direct characterization isn't super reliable. To listen to Prometheus talk about himself, you'd think that he's a righteous upstanding dude who wouldn't back down when Zeus was trying to wipe humans off the face of the planet.
To listen to… well, pretty much everyone else in the play, Prometheus is a hothead whose resistance to Zeus is more a matter of putting on airs than anything else. Or, as Hermes says, he's just a "newly-harnessed colt" who's "struggling and fighting against the reins" (1007-1010).
Whom do we trust? Well, we can't be sure—but, given that we're the humans Prometheus saved, we're kind of on his side with this one.