you don't need to do 500 damage with your character, i did the second badge with the black samurai hitting more than 500, when i finished the game the max hero damage was 176, the best way to do the badges is to start with Sieg, put 50 int, maximixe patriotism and art of war(the rest you put into dex until 120 and maximixe far east weapons to your hero) , go to echigo with 60k, buy 10 black samurais, adjust your first line with 5 black samurai and the second line with 2 black samurais and 3 ghost bowman, and put a lot of bowman and the 2 black samurais in reserve troops. Then when a fight starts you just sit and relax.
On extreme random atack i need the picture to pass twice, it takes 4 seconds to pass one time, and when I score i won 3 seconds bonus... max score = 4 no matter how hard i try. But the normal mode is awesome, when playing for the first time.