FYI I think I hit a few compounding bugs here.Well, you are not supposed to beat her completely to get the card, just dealing 250+ damage overall is enough. It takes good RNG
Bug #1: The triple damage from the 3 slut card continued tripling damage ever single round (regardless if the numbers were above 3 and seemed to cancel out other effects).
This bug made bug #2 possible to find.
Bug #2: I accidently beat Mia instead of doing 250+ damage and losing. It registered as if I lost. Note: Her 2nd health bar was at nearly max health, so if the check is just looking at current health, that could be the issue there.