There's also the Asian "Ranch" near 40th St & Van Buren. It's located near enough to the more Latino-focused Ranch market to cause some confusion, but this one is in the Chinese cultural center near the 202.
They have a lot of seafood. I'm not always sure, however, what is fresh. But at anyplace in AZ, I'm not sure what is fresh. Being on ice isn't a qualifier. After all, Stalin and Mao are still on ice and look o.k.
This store, at least, always has a decent crowd in the fish section, representing a cross section of ethnic folks. Turnover is good at fish counters. They also have 7 or 8 large tanks full of live offerings, so I suppose you can't get much more frash than this. And they'll cook them for you on demand.
My other suggestion would be Sprouts. They seem to have decent fish fare - not a huge selection but what they have seems good thus far.
Fresh, as in still-swimming fresh, fish from Lee-Lee's Market in Mesa (Dobson & Warner) and the shrimp at Ranch Market (Roosevelt & 16th St) have consistently been excellent. (Have not tried any other fish from Ranch Market)
My local Bashas buys from East Coast Seafood. When they order monkfish, soft shell crabs or sand dabs for me, they have been excellent as well.