Choco Mog

Talk to the Chocobo at the front of the farm and reply "Waaark".

Shiva

At the Junon coast after saving Pricilla.

Ifrit

On the boat after beating Jenova-BIRTH.

Ramuh

Lying on the floor in the Chocobo Jockey waiting room.

Titan

In the wreckage of the Gongaga reactor.

Odin

Defeat the Lost Number enemy inside the Shinra mansion safe.

Leviathan

Defeat everyone in the Pagoda in Wutai.

Kjata

Walk to the second area in the Sleeping Forest and it will be floating around. Wait in the spot where it is first seen, then tap the Action button to take it. Do not use against fire absorbing enemies.

Alexander

After the snowboarding sequence, find the hot spring and touch it. Then find the area where you leave markers and keep to a straight path. Find the hut there and enter. Leave through the downward facing door. Go right, find the cave and talk to the person inside. Defeat her and the materia will fall from the sky.

Bahamut

Defeat the red dragon at the Cetra shrine.

Typhoon

Defeat the Ultimate Weapon a few times until it dies. A crate will remain. Go to the jelly object on top of the mountain and its at the end.

Neo Bahamut

After Geas cliff; just pick it up.

Phoenix

Found while collecting the Huge Materia at Mount Condor. After defeating the enemies and the man sends you out to check on the condor egg, it can be found on the ground.

Hades

On the wreckage in the Gelinka.

Bahamut ZERO

Collect the four Huge Materia. Store them in the Observatory, then look closely at the blue Huge Materia.

Knights Of The Round

Found on the island only on the final disc. It is unmarked at the top right of the map, and requires a Gold Chocobo to reach it.

The location and contents of four Materia Caves are as follows:

Materia Cave #1, Knights of the Round

This cave is located far north of the Chocobo Farm and can only be reached by a Gold Chocobo.

Materia Cave #2, Quadra Magic

This cave is located south-east of the Chocobo Farm and can be reached with the Highwind and a Green Chocobo.

Materia Cave #3, HP and MP conversion

This cave is located far West of Rocket Town use a blue chocobo to get there.

Materia Cave #4, Mimic

This cave is located north of Corel and can be reached with a Blue Chocobo.