Look for UFOs to pass by during a battle in the following places (you must have Diablos' "Enc-None"):

1. Outside Winhill Town
2. Mandy Beach, northeast of Timber
3. Heath Peninsula, east of Trabia Garden
4. Kashkabald Desert.

After sighting all four, fly the Ragnarok to the rocky cliffs above the Chocobo Shrine. Encounter a UFO and defeat it. Then,
head to the crater where Balamb Garden used to be. You will encounter a PuPu. Feed him five elixirs and you will be rewarded. Its only a level 5 card, but is definitely the hardest card to find.

Fat Chocobo
Man in front of Balamb Library (Queen of Cards Quest).

Angelo
Watts, on Forest Owl's train.

Gilgamesh
CC King.

MiniMog
Boy running laps around Balamb Garden.

Chicobo
Summon four Large Chocobo at all six Forests, then proceed to
the Chocobo Shrine.

Quezacotl
F.H. Mayor Dobe.

Shiva
Trade "Girl Next Door" to Zone.

Ifrit
Defeat Ifrit.

Siren
Card Master on second floor of the Dollet Pub.

Secret and Minotaur
Defeat Brothers.

Carbuncle
CC Heart.

Diablos
Defeat Diablos (Use the Magical Lamp obtained from Cid to
find it).

Leviathan
CC Joker.

Odin
Defeat Odin.

Pandemona
Zell's neighbors.

Cerebrus
Defeat Cerebrus.

Alexander
Piet in Lunarside Base.

Phoenix
Esthar presidental assistant (Queen of Cards quest).

Bahamut
Defeat Bahamut.

Doomtrain
Timber Pub bartender (Queen of Cards quest).

Eden
Defeat Ultima Weapon.

Ward
Dr. Odine in Esthar.

Kiros
Man in black suit in Deling shopping area (Queen of Cards
quest).

Laguna
Ellone in Lunarside Base.

Selphie
Selphie's best friend in Trabia Garden.

Quistis
"Trepe Fan Club" in Balamb Garden.

Irvine
Flo (QoC quest).

Zell
Zell's mom in Balamb town.

Rinoa
Lose the Ifrit card to Gen. Caraway in Deling City. Win it back
from Marlene in F.H.

Edea
Edea at her house.

Seifer
Cid at Edea's house.

Squall
Laguna at Esthar.