Hey ! It took hours for I achieved the mission. It was difficult. But it's possible ! Now I'm vassal of Queen Daenerys Targaryen :) .
I looked for advices on internet and didn't find. I even tried cheating and didn't manage :) .
So, i give you some advice for making it less difficult.
- Get more than 12 bravo guys at the biginning (I had 15)
- get them in villages near Bravos (No need to go to Bravos, it's annoying)
- go to north of westeros between Castle Black and Winterfell (there are many bandits to fight, and btw you can make money selling prisoners to the Nights watch)
- with money you can pay a sufficient army (cause your 15 guys are not anough)
- save before each fight, so you make sure you can go back if you lose a bravo guy
- make sure you have enough bravo guys (cause going again to Essos for a bunch of them would be annoying and expensive)
- these bravo guys run faster than other soldiers and are less armored, so don't charge too early
- When you have a new skilled bravos (training achieved), don't keep him in your band, let them all in troop quarters, so they will stay alive
- keep doing that during hours (it took me about 8 hours, I didn't count but it was long and a bit boring)

The upgrading is slow, yes, but make them fight and survive. I personnally weakened ennemies with archers before I charge with numerous infantry. And then I charged backwards with cavalry. I rarely lost a bravo guy.
The training skill is useful, i had 3. But the surgery skill was more useful. And wound treatment.
Upgrading speed for me was about one guy per 2 battles. I think I made about 30 battles (i didn't count).

So, I hope that would make the mission less difficult and annoying for you. Well, for me it was annoying, but I gained a lot of money, renow and reputation, so it's ok :) .
Enjoy !