Final Fantasy 7 - Ultimate Weapon

At one point in Final Fantasy VII, Cloud will have lost his memory and will be found in Mideel. When the team is in Mideel, they are attacked by Ultimate WEAPON. When you initially fight, you won't need to destroy it, just damage it a little until it flies away. It flying away is something it'll be doing A LOT later on in Disc 2 or 3.

Later on in Disc 2 or 3, you can chase after Ultimate WEAPON with the Highwind. It will be hovering over a lake near Junon first. Fly into it with the Highwind to initiate combat. Ultimate WEAPON isn't exactly too ultimate. During this fight, just treat it like any other boss battle so far. Cast Wall on your party and MBarrier and keep the party healed constantly. Once you have that down, you can pummel Ultimate WEAPON with limit breaks, spells, summons, and attacks. Once it takes a few thousand points of damage, it will fly away, just like it did in Mideel.

Now, it will move around the World Map. Follow it with the Highwind until it stops. The spots it usually stays at are Nibelheim, Midgar, Mideel, and Cosmo Canyon. As soon as it stops, run into it with the Highwind again to start up combat. After every fight with it, use the Highwind's rest area to heal your party up.

Keep in mind that after every battle Ultimate WEAPON has with you, it does not heal itself. All damage it takes is cumulative. When it takes enough damage, it will head to Cosmo Canyon, where you will fight one last time. When you finally defeat it, Ultimate WEAPON will fall into a portion of the Canyon, blasting it away and opening up the passageway to the Ancient Forest.

Also, for your troubles, Cloud will receive his ultimate weapon, coincidentally called Ultima Weapon. Congratulations!