The first card is Minimog. If you lose that card to her she will give you a Kiros card. You can then win your card back from her brother who is at Deling City near the Junk Shop (he is in black)
The second card is Sacred. She will give you a Irvine card for it and you can get Sacred back from Flo in the mayor's house in Fisherman's Horizon.
The third card is Chocobo. She will give you a Chubby Chocobo in return and you can get Chocobo back from the guy sitting outside the library on a bench in Garden.
The fourth card is Alexander. In return she will give you the Doomtrain card and you can get Alexander back from Timber's pub owner.
The final card is Doomtrain. She will give you the Phoenix card in return and you can get Doomtrain back from the assistant outside of the library in the presendential residence in Esthar
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