Muze is a mono-cats deck is an ok way to do the poison mission (I think that and the occasional greem skeelz deck got me my mission). Only thing is think before you all-in fury Muze. It does 11 damage on Round 1, count their damage first.
Btw, i think it's foolish to waste time going into training room or losing games just to complete missions. just play normally. you'll complete them in due time. and you'll earn clintz and level up along the way so all is not wasted.