I ended up answering my own question. I finally encountered Algol on my 4th run through the Extra Route in Arcade mode on the Easy difficulty setting. His appearance in Arcade mode seems to be random, and the chance of him appearing seems very low. When I finally encountered him, I was using Leixia and Algol appeared as the 5th opponent. I was about 25th level at the time.From what I've seen so far, all the equipment unlocks are tied directly to level advancement. It doesn't seem to matter how or where you level-up.
I tried the Extra Route in Arcade on the easiest setting and Algol did not appear. Does it require trying it at normal difficulty, or is it random?