How to get four Ultimate Weapons on Disc One of Final Fantasy VIII:

Squall's Lion Heart:

1x Adamantine - Card Mod Minotaur
4x Dragon Skin - Low level Grendels on the side wall of the Yaulny Canyon
12x Pulse Ammo - Get 20 Elnoyle cards from Trepe Groupie #1, converts to 2 Energy Crystals and then 20 Pulse Ammo.

Zell's Ehrgeiz:

1x Adamantine - Card Mod Minotaur
4x Dragon Skin - Anacondaurs in the SEED exam
1x Fury Fragment - Card Mod 4 Blue Dragon cards from Girl in Balamb

Selphie's Strange Vision:

1x Adamantine - Card Mod Minotaur
3x Star Fragments - Card Mod 9 Iron Giant cards from Trepe Groupie #1
2x Curse Spikes - Card Mod 2 Tri-Face cards from any level three card player, Friend of Trepe Groupie #1 or Girl in Balamb

Quistis's Save The Queen:

2x Marlboro Tentacles - Card Mod 8 Marlboro cards from Trepe Groupie #1
4x Sharp Spikes - Card Mod 4 Grand Mantis cards from Trepe Groupie #1
4x Energy Crystals - Card Mod 40 Elnoyle cards from Trepe Groupie #1 and convert to 4 Energy Crystals