This game is also available on PC.
Irvine Card - Part of Card Queen Quest(not Card Club)
Kiros Card - Part of Card Queen Quest(not Card Club)
Languna Card - Play Ellon in Space(last chance)
Ward Card - Play Doctor Odine(while you are Languna)
Siron Card - Play owner of pub(in Dollet)
Shiva Card - Give nude magazine for free to the man on the white SeeD ship.
Laviathan Card - Play Jocker(Card Club)
Pandimonea Card - Play hotel owner(Balamb)
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When they have a small square will appear in the bottom corner during their attack. Press square when it appears to boost their power, but make sure you stop when a red-cross appears or it will go down to nothing.
this works even better if you have a auto-fire pad, so long as you remember to stop when the red cross appears.