Squall's Lion Heart Ultimate Weapon - FF8 Guide
The Lionheart is Squall's Ultimate Weapon in Final Fantasy 8. Unlike many of the other games in the series, there is no fancy quest or even location to find this weapon. Throughout Final Fantasy 8 there are Junk Shops and at these shops you can trade items to them in order to receive an upgraded weapon. That's how you retrieve Squall's Ultimate Weapon.
You can obtain the Lionheart during Disc 1 while you're in Deling City. In order to do this though you'll have to go out of your way quite a bit so that you can get Pulse Ammo soon enough. You can either play enough Triple Triad to get enough Elynoyle Cards to Card Mod into the Pulse Ammo you need or level Squall, Quistis and Selphie to 30+ and have the Mug Ability on Diablos.
Assuming you don't care about obtaining this weapon that early, during Disc 2 you will have plenty of opportunities to get the Pulse Ammo you need.
Required Items for Lionheart:
4 Dragon Fang
12 Pulse Ammo
Adamantine: Card Mod the Minotaur Card for 10 Adamantine items. This is the earliest possible way to acquire these items, if you wait until later in the game they become more common.
Pulse Ammo: The earliest to acquire this item is during the Laguna Dream Sequence outside of Galbadia Garden on Disc 1. Mug Elastoid enemies during this Dream Sequence for Laser Cannons which you can then use Ammo-RF on to turn into Pulse Ammo. To do this you'll have to make sure your party is level 30+, as only the level 30+ Elastoid enemies drop the item you need.
During Disc 2 when you're in control of just Irvine during the Fisherman's Horizon & Balamb Garden "Band" Story Scene you can collect 5 Pulse Ammo. There is only a very small window of opportunity you can collect the Pulse Ammo from here too.
Other ways of acquiring Pulse Ammo:
Energy Crystal (Ammo-RF) - Easiest way to get these is later during Disc 3. Card Mod Elynoyle Cards (Esthar Elynoyle Farming Location)
Power Generator (Ammo-RF) - Aside from Blitz enemies, the easiest way to get a Power Generator is from Lunatic Pandora on Disc 3. if you didn't open the appropriate hatch during the Laguna Dream Sequence on Disc 1, this Power Generator will be unavailable.