Mostly B. A would be understood and is probably a flub that a lot of us native speakers are guilty of, but technically incorrect I think. Not likely D, since "daren't" is either not even a valid contraction or at least very uncommon (Edit: In my dialect, that is; I don't know about others). I'm not sure about C, because it's an uncommon phrasing, but I think it should be "dares not", not "dare not". That manner if speaking is practically archaic for words other than modifier words like "do" and "would", so I wouldn't use it anyway for the most part.
I can't think of many realistic situations where climbing a tree would be such a huge risk that it would call for this phrasing, though. The situations I can think of are if the tree is unstable and on the verge of collapsing (i.e. climbing the tree could get you seriously hurt), or if the tree is owned by someone who would punish you severely for doing so. On the other hand, if someone is just afraid of climbing trees, you would just say something like, "He is afraid of climbing trees." or, "He doesn't like to climb trees." Something like that.