The issue you raised does not distinguish A from C. Both answers basically say "G. served his way out of the break against A." I don't think there is a meaning problem there, since it is in fact what the author intends to say.

I have a problem with the sentence in general because one doesn't "give" an expression; one "has" an expression. Nonetheless, C is much better than A. Let's examine C more closely

C) Giving an expression, G. served his way out of the break against A., who is agile.

blue: modifier describing G.
brown: object of verb "to serve". when it is ignored, the rest of the sentence should make sense
blue 2: modifier describing A.

At its core, C says "G. served against A". It is simple and clear.

Conversely, look at choice A.

A) G. served his way out of the break giving an expression against the agile A.

brown: object of the verb "to serve"
blue: modifier trying to describe G.. Here we have a problem because the modifier is far from G., making the sentence more difficult to understand. Typically, when an -ing modifier is not separated from the rest of the sentence by a comma, it modifies the word that immediately precedes it. For example, "I don't like people jumping on my bed". The modifier describes "people". In the case of answer A, the placement of "giving" suggests that it would modify "the break" when in fact the author is trying to modify Goran. That's a problem.