no. there's no health bar.

but Prince will behave differently after being hit:
1st hit: not knocked down, just being pushed back a bit; may hold his right arm/waist with his left hand. still standing upright
2nd hit: knocked down, jump right back up; hold his right arm/waist with his left hand, posture starts bending down a bit
3rd hit: knocked down, takes him longer to get back on his feet; hold his waist with his left hand; corners and sides of the screen turned red - next hit can pin him down for good
well, I am still in the v. beginning of the game so this may change: initially one hit is enough to get Prince "red cornered". Elika saves Prince all the time though, so I don't know if Prince can actually die... :\
oh, and make sure you use that "dialogue" button during boss fight too - Prince may bad-mouth/taunt the boss, flirt to Elika, or just say some random stuff
