I took a different approach than the other two posted. I used Dragon (the Bruce Lee looking fellow, 2nd character going left to right in the Character Select screen). I also played NORMAL game.
I used two different moves (BTW, I suck at fighting games, call me spam-a-lot LOL). When the match starts, I kick low and try to trip up my opponent. I try to kick then move forward. Sometimes to speed things up, I throw my opponent with
. There is more damage to be inflicted, but sometimes you can be attacked if you aren't careful. If all else fails, try to block the attacks, stun them, or wait for them to be vulnerable.
I scored 300k by the end of the 1st bonus round (2 fights and the bonus). You don't have to be perfect, but work fast because of the 5 min. time limit and most importantly, every round you win gets you 1000 points per second remaining (i.e.: 50 seconds * 1000 = 50,000). The health bonus is puny compared to this. The bonus round works the same with time bonus.
I recommend trying to have 300k at the end of the bonus stage. The 3rd stage goes up in difficulty and there are NO continues if you lose in Caravan mode, so keep that in mind.
You have more time than you can imagine to do this, so play smart. You have no need to panic.
Good luck.