Disregard tiers, yes, but remember that Mina beats Taki for free. You may as well exploit her one and only good match-up.
Aside from that, I think that Mina in a tourney may not be so bad. I mean, she's bad, but I think she's better off in a tourney environment, if only because your opponent will probably make the mistake of not pitbulling all over you, and if you give Mina some space and time to work, she can win games. I also had some very tight (for me, and for Mina) matches with Vint's Sophie recently that made me think twice about Mina and how I was playing her. She can actually do the safe thing pretty well, and you have to play safe against against Vints. :/
Anyways, for matchups, to be on topic, I've been having a hell of a time with Cervy. With Mina and with Rock. I think it's just a terrible matchup, really. He can effectively punish so much of what Mina does, not for Sophie-damage, but at least as consistently, and his fast mids are a pain to deal with. Add to that his TJ options for moving in and you're forced to stop using 4A for spacing, which is a bad spot to be in. It also helps that the only 2 Cervy players I've played against are just much better than me right now, and that I don't know dick about him as a character past that I don't like him and franman gets 80% of his iGDRs out.