Aeons Soul

I am currently replaying FFX and i'm up to the point where you defeat seymour for the final time. At this point i realised that i forgot to battle belgemine on the calm lands and thus did not receive the aeons soul key item which lets you mess around with the aeons' attributes. I went back to the calm lands and she wasn't there anymore.

Is there any other way i can get the item???

Remiem Temple. You must train a chocobo enough so that you can ride it around the Calm Lands (complete the first challenge sucessfully). Go to the south entrance, and take a right, until you see a Chocobo Feather. It will jump across, and you will be able to enter Remiem Temple. From there, talk to Belgemine inside the Temple, and defeat one of her Aeons.

It SHOULD drop the Aeon's Soul, but if not, the item itself is not necessary, since the improvement costs are VERY costly, unless you are playing a version where your characters have the Distills.

There are versions where there are no distiller wepons?

NTSC and NTSC-J do not have Distill weapons or skills, only items of the same name.