you should try mystic arts, some are really good (torin would say he hates hexes...!) and can deal a .lot of damages. and if you want to trigger arcanas, you really have to play mystic with a few charas.
You can either go pure Mystic, or Combat Art oriented with a dash of support skills on the side.
For the former, choose Mystic route. (obviously)
For the latter, choose Combat route, if only to get a bonus to increasing STR and/or combat arts (both of which she desperately needs training on). For this route, I HIGHLY suggest you temporarily turn off all mystic arts and work on her lotions and even her traps. This is because her default class makes it rather difficult for you to train her in combat, so changing her class to either Wanderer or (preferably and most probably) Hunter would make her combat training more effecient in the long run. And hey, you need Hartshorn on her anyways for revival.
Granted, I dunno if choosing a character's 'focus' (combat, mystic, balanced) affects their growth at all, but until someone digs into the code, better be safe than sorry. If you're going to use her as combat, all the spells you're going to use from the mystic line don't need INT anyways for the most part (her base INT I find is high enough), so you have nothing to lose by making her combat focused.
In any case, Irina excels at either of the two, as long as you focus either on Mystic or Combat as her damage art and never both at the same time. One caveat though is that Irina's non-remnant weapon just plain sucks, so unless someone can confirm the rumour that she asks for Superlative Tataraichi, you practically have to give her Nightbloom in order to pull her own weight in the end game.
Turn 1: Enhance Spells Turn 2: Overdrive, Water Blast X5
"so unless someone can confirm the rumour that she asks for Superlative Tataraichi"
She doesn't. And mikeyakame is right, focus just determines what types of accessories they request (and without modding TLR.exe, there are only two real choices, as mystic=balance in the unmodded version) and which weapon upgrade path they use. Obviously if you give her Nightbloom, focus only determines the type of accessories they request.
I can send you a patched tlr.exe with bugfix for mystic focus accessory requests if you like. Feel free to shoot me an email at email@example.com if you want one. It was suttyo and myself who figured out the problem and how to fix it in the first place so it's all good.
Same goes for anybody else who wants one. Just let me know your forum nick in the email so I know who I'm dealing with.
It won't be an original .exe though that is why I can't post it here, but I have no problems giving you it offline from here. I won't patch an original .exe because of the steam protection, from what i've been told it doesn't like when the original .exe is modified and I have no intentions of dealing with random bugs because of such protection either.
It can be done easily with a hex editor but if you rather a pre-patched .exe that's fine by me. Torin and a few others all use it and it works well. Characters with Mystic focus request Mystic focus accessories like they should.