According to HSReplay, Midrange Hunter is 59% versus Big Shamam
What is the overall strategy versus Big Shaman? I find that it is quite hard to develop minions on the board with their removals. They can develop boards somewhat effectively too with Muckmorpher, Rain of Toads, etc.
I find that I usually scrape a win only if my Zul'jin is able to cast Dire Frenzy on my beasts (usually by Zul'jin also casting Animal Companion since I won't have minions on board when I play Zul'jin)
Big shaman is a slow deck so you have all the time to develop your minions. As a midrange hunter, you have enough resources to threaten control warrior with its infinite removals, so it can't be more difficult against the other decks. Going face is useless. Big shaman has fountain, brew, zilliax so it will heal to full life easily. The goal is to control the board and hit face once there are no more minions on board. Your opponent won't be able to cast multiple spirit or voodoo on his minions if he has an empty board. Keep your deadly shot against the huge health minions like ysera. Only dire frenzy the wyverns from unleash the beast, if you go to fatigue you'll win, so you don't need to rush and dire frenzy weak beasts like a paw or a wolf. Against a slow opponent, you don't want to pollute your deck with dire frenzied beasts before having your key cards in your hand (master's call or zul'jin), so try to have at least zuljin or 1 master's call before casting dire frenzy.