Boss Rush is a challenge in Death Wish Mode. Like the title suggests, you have to face all 5 bosses, with no healing in between!
As stated before, in this Death Wish, you must fight all of the non-EX bosses in the game. This can be a hard task to achieve, especially without healing between fights. However, it is still possible to heal with the Heart Pons occasionally dropped by the bosses.
The first bonus adds to the Death Wish's difficulty by requiring the player to hit the boss they are fighting every time they are vulnerable. This forces the player to have quick reflexes so this bonus can be achieved.
The second bonus makes this Death Wish harder by not only banning healing in between fights, but by decreasing the number of Heart Pons significantly.