You might own a few "Occult Fan"- magazines. Unlike the Timber Maniacs, they're not only to read for your amusement: they give you hints on how and where to get a rare card. You need the Ragnarok for this quest.
Sight all UFOs by going to the places the magazines mention and junction the Enc-none ability so you don't encounter any monsters. After a while, a UFO will attack you. Yes, a UFO. o.o
1. Mandy Beach- Remember the small river near Timber? Follow it until you reach Mandy Beach and run around until you find the UFO. Yes, you may trust your eyes, he's stealing one of those heads from the Easter Island...
2. Winhill- Simply run circles around the town (outside on the world map). After a while, a UFO will appear. This time, he's kidnapping a cow. Yes, a cow. Don't ask.
3. Kashkabald Desert- The desert is south of Esthar, somewhere to the west of Cactuar Island. Run around until you find the UFO.
4. Heath Peninsula- To the east of the icy plains near Trabia, you'll find a small peninsula. Land on the small island next to it. Again, run around until the UFO appears.
5. Grandidi Forest- South of the Heades- Island you'll find a Chocobo forest. Land on the cliff to the north of it and fight the UFO until it crashes.
6. Alcauld Plains- Go to the place where Balamb Garden once stood (back in the days when it couldn't fly). It's now nothing more than a brown spot. PuPu will fight you.
PuPu has only 10 HP, so be careful not to kill him. Instead, give him 5 Elixirs and he will give you the PuPu card- the rarest card in the game. You can modify it to a "Hungry Cooking Pot" which makes a GF learn the "Devour"- ability. See the Devour List for more information.
If you don't have 5 Elixirs or have just more fun killing things than receiving rare cards, slice PuPu up (which is what I did. He looks so cute with the Xs in his eyes ^^) and gain the "Accerelator"- item. That wouldn't be difficult because all he does is saying "I want Elixirs!", and he only has 10 HP...