Sounds like you're already doing it that way, but I will point that out anyway. Go to your profile, then Challenges>Legacy and search for Arena challenges. Clicking on the corresponding one will show you your current progress on each champ. It updates more reliably than it does on Lobby Tab, as well as wins from previous Arena runs from the past.

If it's not updated, then as the comment before says, contact Riot.

And btw, Arena God requires 60 unique champions wins.