Can you only pass on a skill through breeding if you leveled up the parents and got the skill even they would have learned it?

uhh what do you mean?
as in can you only pass a parents skill on to a monster through breeding if they dont know the skill you want to be passed on?

When you breed monsters, the offspring will be able to learn the skills that its parents can normally learn, regardless of whether or not they have learned them yet. I have also found, that they will take longer to learn their parents' skills if their parents did not learn them before breeding.

Note that monsters that you have bred do not learn the basic skills from their "grandparents", if any. In other words, they will only learn the basic skills from the most recent generation. On this point, I am 99% sure. I could be wrong Hard to claim to know everything about this game. Hope that helps.

\m/

for exapmle:metalkings can learn hellblast if u breed 2 u get gold slime but it wont learn hellblast unless u trian metalking to learn it before u breed