How ‘illegal’ is she? Did she come here on a valid permission previously and then the permission expired? What did the permission expire? Or did she come into Ireland on a short-stay tourist stamp? Or no stamp at all (e.g. by crossing from the North)?
In almost all cases, since she is undocumented at the moment, she will need to apply to the SOIN Unit to try to get a valid permission. The chance of getting an approval will depend on her genuine your relationship is, your financial situation, among other things.
I don't have any experience to share, but this is pretty standard stuff that doesn't require someone's personal experience. If she has a legal permission, she gets a Stamp 4 right away; otherwise, she needs to apply to SOIN unit. Simple as that.
She will have to go through the same process I went. She won’t get a visa from the immigration in dublin, she will need to send her application to the SOIN division. I did my application myself, but I was only a few days with my visa expired.
If I were you I would involve a solicitor, principally if she has been at work during this time.