You can only beat Ultimate Weapon after fighting him in the mandatory boss battle in Mideel. After this, you should find him hovering over a crater near Junon (if he is not here, then he may be flying around the map, in which case ram him four times with the Highwind and follow him to where he stops).
You will have to fight him a bunch of times as he escapes the battle after a set amount of damage. You will have to chase him around the map in the Highwind and ram him until he flies off to a location. It takes four rams for him to do this. Anyway, once he has received enough damage, the final location he will fly to is Cosmo Canyon.
Once he is here, fight him one last time. Be warned, as the player who kills him will have Shadow Flare cast on them when Ultimate Weapon dies (it is a good idea to have Enemy Skill equipped on that person). Once he has been defeated, he will fall into the earth and leave a big crater (allowing access to the previously inaccessible Ancient Forest).