I didn't think Parasol had any materia slots? Princess Guard is her best weapon. It may have less attack power but it has the special effect that I think all Ultimate Weapons have.

The weapon is called Ultima Weapon and it drops Cloud's Ultima Weapon if I'm not mistaken.

I searched FFCitadel for Tsurugi and nothing turned up.

That's all I can be bothered to type right now.