In terms of story Iria is reasonably basic: coming of age combined with hunting the unstoppable monster, mixed with a heavy dose of corporate corruption .
So you have the cool mentor  who gets wiped out in the first episode, the lead character struggling to come to grips with being alone, and then has to deal with the monster once and for all in the finale. Naturally the authorities are incompetent or corrupt so all the responsibility falls on the lead character.
What lifts Iria far above the average for this sort of story is Iria and the world she lives in.
In the first episode, Pitch Black, Iria is identified as an apprentice Hunter and gets into a certain amount of trouble as a result. However even her early failures demonstrate her skills and raw ability: not only is Iria an Action Girl, she is a fully justified example of the trope.
This means that we get to see some genuine character development, as well as some serious training, as Iria toughens herself for the finale. The Iria of Wind Song and Shangri-La is solidly based on, and grown from, the Iria of Pitch Black and Rampage 
Toss in a moderately quirky set of supporting characters and Iria suddenly has a lot to offer beyond the basic plot.
Then there's the truly wonderful world building and the design work. One problem with science fiction can be the tendency towards a dated future  when it looks just like today with spaceships. Relatively few works get this right.
Iria dodged the issue completely by building a completely different world. The world was meticulously thought out, and still looks as fresh and intriguing as it was when I first saw it.
The combination of the characters and the world is what really makes Iria sing as a series.
Finally the monster, Zeiram, is one of the best I've seen in a long time.
There is some bad news: Ms Fanservice come on down. It isn't overdone too much, but there's enough to be mildly irritating.
Second is the somewhat limited features of my DVD copy. There was a period where early DVD releases basically consisted of stringing the VHS releases together and adding chapter breaks.
This means that you only get the credits every second episode, which is a real shame, and there are no extras at all.
This is still a series I enjoy a lot, and the option to treat it as a movie by watching in a single sitting is an attractive one.
I'll wrap up with the wonderful opening credits:
 Which I suspect was strongly influenced by the Alien franchise.
 Well, mentors actually, and one of them comes back... sort of.
 The middle episodes are Visage and Broom Tree.
 1st link is Gunbuster, 2nd link is The Rolling Stones.