|Of all blue mages, I find Tailtiu to be one of the most flexible. Her statline is fairly potent, she has high availability as a 4-star unit, and she doesn't have a prf weapon forcing her into a specific niche. And, as a blue mage, she can easily decimate the endless supply of red units in the game.
To begin, we'll discuss her IV spread. As an offensive unit, her attack and speed should be prioritized over her defensive stats. Depending on the variation of the build you go with, you'll want different boons; as for a bane, she'll always prefer a defense bane over anything else. If you choose to utilize Brazen Atk/Spd or can reliably buff her speed with allies, an attack boon should help push her into more potent territory. If you choose standard Life and Death and don't have speed buff support, she'll likely want a speed boon to compensate. A defense bane would be the most useful to her, however an HP bane can help lower the Brazen threshold.
Her weapon will likely be the most difficult thing to find; the Juicy Wave+. You'll have to pry it from a Summer Camilla, though its built-in Desperation will prove a key feature in this build. Refining it for speed will be the most useful.
Her assist is totally flexible. Her built-in Rally can be used to score slightly higher in Arena over a movement assist, if I'm not mistaken. As for her special, a 3-turn count special will be prime. Draconic Aura can be used for more consistent damage (Roughly 17 points of damage when in double-Brazen range, sans other buffs), while Luna may provide good res-tank-cutting territory. My Ishtar finds herself in a similar condition choosing between the two, and I must say Draconic Aura is significantly more reliable. That said, I'm just writing this on a website. I'm not a cop. Live your life.
Her A-Skill provides some options. The best option is Brazen Atk/Spd, as the HP threshold from that is practically the same as that of the Juicy Wave+. And this skill is not unreasonably rare; it can be attained using some heroic grails and some feathers to promote a Linus. However, it still is pretty expensive. A cheaper alternative is Life and Death, which can be found on a 4-star Sothe. Just note that it will put her in risky physical range with a physical soak in the low 50's. Her Seal should be Brazen Atk/Res to just further her damage output more. Likewise, you may use Atk+3 for reliability's sake.
Her B-Skill will likely be the second-most difficult thing to find: Special Spiral. While currently only found on Lewyn, he IS in the regular 5-star summoning pool, making him slightly less rare than Summer Camilla. The main catch with Special Spiral is that it takes up the B-Slot, making it compete with skills like Desperation and Vantage rather than synergizing with them. However, there are three Desperation weapons in the game (Maybe four or five, if you count prf weapons): Juicy Wave, Fishie Bow, and Starfish; the Sketchy Summer weapons. Thus, this is a work-around for this competition between skills. In a similar sense, this build can be run on dagger and bow units as well, given the fodder. Though the units who originally possess these weapons are prime candidates to begin with. Thus, this is where the gist of the build is. Special Spiral reduces the Special count to essentially 1, and the Juicy Wave+ will allow Tailtiu to attack twice (one of which will be a special proc).
Her C skill is flexible as well. Def Smoke may help physical allies in the Arena score some kills. Atk or Spd Wave can be used to bolster her offensive prowess. It depends on what you have and what you need from her.