Attack and Defense

This team comprised of ridiculously rare units pays off quite nicely. With the right skills, you'll plow through Lunatic no problem.

Corrin's Dark Breath+ is a lifesaver as it debuffs everyone with Attack and Speed - 5 within a two space radius. This is great for Lucina, Azura, and Takumi because of their high speed. And with Hone Atk 3 and Rally Defense, you'll be taking quite a few hits. Corrin is very bulky with an amazing 40 Atk stat. (At least mine is)

Azura is pretty self-explanatory. Just Sing a lot. But she can be used for more than just transferring her turn to other Heroes. She practically eats swords for breakfast and has red tomes for dessert. Despite her thin defenses, she's actually great for taking sword units as they will do literally 0 damage. And red tomes hardly effect her because of her resistance.
Takumi is an amazing unit for this particular Tempest Trial. Simply because there is this one map with just flyers. They drop like flies around him. Takumi is also good for finishing enemies he wouldn't normally one shot. For example, if Lucina attacked a Blue Mage for example and couldn't kill them, she'd still do enough damage for Takumi to finish. I recommend putting Desperation on Takumi as it will allow him to double a lot of units.
Finally, we have the glass cannon herself, Lucina. Lucina is one of the bonus heroes that gives you a lot of points, even if you lose. Lucina is the bane of Veronica's life. With a whopping 50 Atk (53 if she has Fury 3) she can just one shot any green unit and a lot of red units. However, she is frail so I recommend you give Rally Defense or Fortify Defense to another unit so she can take more hits.

Corrin (F)

Azura

Takumi

Lucina