Upgrading your party's weapons to their second form should be fine. This shouldn't take any "big bucks" really. Upgrading to the final (third) form takes a lot more time and farming to do. I haven't done it myself yet so I'm no expert on how... But it would be kind of overkill to do it just for the story's boss.

On the other hand, getting the final forms for your weapons would be pretty much a necessity to beat the last few hunt missions.