I haven't read or watched Berserk, but I'll give a shot at answering the question.
I'm assuming that this quest-for-vengeance isn't portrayed as wholly positive; something like that has to affect a character in some way; if nothing else, it changes the way they react to things, as well as their perception of the world.
People have ranted and raved about characters like this don't work, so... why does it work in Berserk?
I rhink it's a matter of whether or not he's had something to live for before he set out on the quest, and whether or not the quest has changed him/been detrimental to him in some way.