According to Merriam-Webster, steadfastly, means in a resolutely or dutifully firm and unwavering manner. Meaning in this case, steadfastly bent is strongly motivated towards a certain topic. A synonym may be "hell-bent" meaning determined to achieve something at all costs. And within the context of the text, the narrator is describing the determination from Krishna's point of view of the other characters and the bloodshed.

Steadfast has a connotation of some courage and positive moral uprightness. I feel like "zealous" would perhaps have been the better word to emphasize, here.