High Summoner Galatea:
I have several suggestions regarding opponents - there are quite a few folks who may accept your challenge if asked.
First, you should try and contact Summoner Almors. He has been sick lately and is recovering on Talking Island.
You should also try Summoner Basillia. I have heard that she is busy researching a new form of Summoning magic near a farm on the southern shores of Gludio.
Summoner Camoniell, of the Elves, has been in seclusion in a cottage in southern Dion. I've heard he has had some trouble lately.
Summoner Celestiel usually resides in the Ivory Tower, but has returned to the Elven Woods on urgent business from her homeland.
Summoner Brynthea and Summoner Belthus of the Dark Elves may be proper opponents for you, but they are hard to find, as they are not likely to stay in one place. Last I heard, Brynthea was somewhere in the northeastern parts of Giran, and Belthus was somewhere in the Cruma Marshlands...
These Summoners are all proud and haughty people, and may scoff at a challenge from an apprentice Summoner like yourself. But, at the same time, they will likely accept your challenge, if only to display their supremacy over you.