The Ultima Weapon starts out as a Toy Gun/Model Gun. 15000gil later it becomes the Silver Model Gun. 35000gil later it becomes the Gold Model Gun. And finally, 200000gil later it becomes the Ultima Weapon. I'm pretty sure you can upgrade this gun during a level, but if that's not working for you, try upgrading it between levels.
I really don't remember Grimoire, I haven't played in a while. If you're short on gil, try the defeat 100 enemies mission in mission 9 I think. Each time you complete this, you should obtaim 40000 gil & the Golden Moogle Doll, which has no other purpose other than being sold for 37500.