Iria is a bounty hunter, as is also her brother Gren and few of his friends.
At the start, they were supposed to free a station by freeing its transmiter station beforehand. They had to fight battles and battles until they were able to do this, but only then did they find that all of the hostages were long dead.
Then Zeiram shows up.
Zeiram is an alien being, dead set on destruction. It has the abilities to meld with any weapons to make up for any body parts it might lose at any time. Needless to say, it seems like it would be pretty damn close to impossible to beat such a thing.
Gren ends up giving up his life in order to let the other memebers of the team get away. From here, Iria leaves and heads back to her home planet. Not until later does she learn that Gren has become possessed by Zeiram itself, and she must kill him in order to kill Zeiram. Hence her destiny comes into view; brother against sister, stopping only in death.
Iria begins to ponder her destiny as she waits for the final showdown between herself and Zeiram. I have to agree with her hesitations and doubts on this one. What kind of cruel fate would make ones destiny be the death of a sibling? It just isn't fair.
But no matter what happens, no matter what is through at her, Iria is always graceful and sturdy, never the one to take orders but rather always the person who gives them.