Hikaru's magic is based on fire, which is not a surprise for any of us, due to her fiery presence. Her main magic spell are two, at least you meet those in the manga.
Arrow of Fire (Honoo no Ya) - this is her most common spell at least in the manga you see her using it few times. The fire takes a form of an arrow and goes directly to the intended target burning everything when colliding with it.
Crimson (red) Lightning (Akai Inazuma) - this is what we can call the ultimate attack, the strongest one used by Hikaru during her travels. In the manga I think she uses it once, I'm not sure about it, but if I remember well it's during the battle against Zagato.
She had two weapons during her time in Cephiro, the first one is the sword (the sword chose her because Hikaru is really good at Kendo, and that's the kind of swords that she should be good at using) that Persea lands her so she can defend herself while on her quest for the mineral Escudo, the other one is her personal sword, that only she can use. If anyone else touches it, it becomes fire and burns the person trying to use it.
Hikaru's personal sword is also somehow like her armor, it evolves during the trials. The base one is blend, but still nice to look at, all the evolutions have the same colors combined which is red and golden. Looking at the images as I said the first look is quite plain, then after the water shrine it seems like it slowly opens like a flower, it looks much more decorated, and then on second evolution, after the air temple it gets other details, but it looks like a closed flower or maybe an insect with legs. The last evolution is where the sword gets its final form and opens up, showing all its beauty. Maybe more than a flower, it does look like a flame.