this may be glich my not but on my ver the bosses always have same hp take odin for example i attacked him on level 20 odd and he had 8000 odd hp and he beat me then i attakcend him on level 40 and he still was on the same level with same stats and had exactly the same hp as befor i encounter this with all bosses with the exception of diabls as he is classed as a monster battle only monsters level up wiht you not bosses

oh and for the seeD exam it starts when you are told to go to the fire cavern and ends once the annuncment is made for who made it into seeD more info if people ask.