It'll be hard, but I'm certain that it's possible. Gau's rages should help, and so should Stragos lore. Also, never underestimate the importance of good equipment.
I passed Phantom train. I didn't feel like coming up with an actual strategy for him, so I used a phoenix down. I figure that I'm not going to get many opportunitys like this, so I might as well take them while I can. Rizopaz beat me once too, but he wasn't really difficult at all. So far I've run into at least some trouble with every single boss with the exception of Whelk.
Right now I'm gathering gil in the veldt. It seems that in every challenge you are forced to spend alot of time doing something very tedious and very boring. My goal is 40,000+ gil, and right now I only have 18,000. A few more hours should net me that 40K though.
Edit: The guide I'm using advises me to get three white capes. I already have one. How necessary do you think this is? I'm at 36,000 gil right now, and my goal is 40,000. 2 white capes costs 10,000 and that takes a long time to get. Should I actually buy the two white capes? How long will it be until I have the airship, because if I can hold out on buying these things I will.