Bought from Battle Square in Gold Saucer for 32,000 BP
After the huge materia episode in Corel - If you saved it from the train, then go into a hut in the northwest part of the town. Talk to a woman there and she'll give it to you.
First, make sure you have Tifa in your party, then go to Nibelheim. Go into Tifa's house, into her room and go to the piano. Play the highwind theme on that piano with the following sequence: X, Square, Triangle, Triangle+L1, Square+L1, X, Square, Triangle, X+L1, O, X, Square, X, Start. Cloud will ponder for a while, before Tifa goes on about sheet music. She'll find a letter, read it and then jump around a bit.
This one is a bit tricky and should be gained as early as possible on disc 1: After gaining the buggy � go to Junon and get the boat back to the Western Continent. Head North-ish until you come to a river that you previously couldn't cross. Go into the cave and speak to the man. Here's where it'll get annoying: if the last digits of you total fight counter is equal (say 311 or 155 the man will wake up and give you some Mythril) if not, then fight until you do. After this � head back to Eastern Continent and look for the house that's on its own. Go inside and talk to the bloke inside � he'll ask you if you have any Mythril � which you do. Give it to him and he'll give you a choice of either a big or small box. Choose the small one by going upstairs and going to the left � there you'll get the item you need.
Getting this limit break is actually pretty simple: first go into Nibelheim mansion and go to the safe -- open it using the combo Right 36, Left 10, Right 59, and Right 97 and then fight "Lost Number." Beating it will get you a key, the Odin materia and also the Cosmo Memory item.
Go to the Sunken Gelnika once you have the sub and enter the cargo hold. It will be on the bottom part.
Go to Wutai and beat Seven Shades of Chi out of the Pagoda Masters. Godo will then give you the item you need.
Kill 40 enemies.
On the Western continent is a pool of water with a waterfall; get a chocobo and go under the waterfall with Vincent in your party. Inside, you'll meet Lucrecia and some stuff will happen. After this, you'll be back outside. Fight for a while, and then go back inside the waterfall. Run up to the "throne" and Vincent will find his ultimate weapon and the item he needs.