I did this on the GBA in about a month, because I saved before each room and if I didn't get one, I just started over from the save.
Obviously, the PS2 is a different story, because you can't carry it around with you and it would take so long to restart. Thankfully, the Roulette cards and Roulette Rooms make up for any lacks of high-enemy-card-chance room cards.
The last heartless defeated is the one that drops the card, as always. If you were to get an enemy card, it would be of the last heartless defeated, so make sure so save the one you wish to get till last.
The chances are originally 2.5% for an enemy card, but Teeming Darkness, Almighty Darkness, Looming Darkness and (possibly?) Bottomless Darkness all increase that chance. I don't know what it goes up to, but always make sure to do your battles in those rooms.
I have been playing much longer than I was on the GBA version and I'm only on floor 5 because of the enemy cards....
The treasure room cards will also usually provide something good, sometimes powerful enemy cards.
Are you talking about Lexaeus, Zexion and Ansem? Or the Key to Rewards Rooms, which give KH2 Organization member cards? Because I can tell you right now that the only way to get enemy cards is through battles....