I know most of my information is based on the manga, but not a whole lot
is said about Galaxia in the anime. I am basing the information about what
she is the
"soldier
of" on the manga, because well, that is the only place where anything
about it is directly stated.
Several times in the manga Galaxia is referred to as being the Soldier of Destruction. She even states it herself.
"I trust my golems put on a great performance for you? I am the galaxy's ultimate soldier of destruction. Welcome to the castle of Sailor Galaxia, Sailor Moon."
Of course a lot of people associate Sailor Saturn with destruction powers.
While she does have the ability to end life, I believe it is more of a "destruction"
at an appointed time, instead of Galaxia's "chaotic" sense of destruction.
Following the idea that Sailor Moon and Sailor Galaxia are opposites in a sense
also makes the destruction idea
more
plausible.
"Soon I will have the most powerful sailor crystals in the galaxy, I have both the galaxy's most destructive, the Saffer Crystal I carry, and the infinite power of rebirth in Sailor Moon's Silver Moon Crystal..."
Sailor Moon's powers can pretty much reverse the effects of Galaxia's. There are also subtle themes in the manga which suggest that in order for "rebirth" to take place destruction has to before hand.
Now on to solitude.
Sometimes Sailor Pluto is called the "Soldier of Solitude" but never once is she stated to be so in the anime or manga. In the Materials Collection Artbook, Galaxia is in fact called by that. Galaxia does fit the "solitude" idea, in the manga at least. She was born alone on her planet and lived in solitude for quite sometime. Pluto as being guardian of the Time Gate did have to stay alone, but wasn't always.
Galaxia could be called by either term, but it is uncertain which she really is, maybe both?