Trying to keep her balance on the icy surface,
the last competitor's ski-tip caught the pole and somersaulted into the soft snow.A. the last competitor's ski-tip caught the pole and somersaulted into the soft snow.
Since modifying phrase has 'her', the main clause should refer to 'her' and so, it has to be noun and not a possessive.B. the ski-tip of the last competitor caught the pole and somersaulted in the soft snow.
'her' cannot be the corresponding pronoun for 'ski-tip'C. the last competitor caught the pole with the tip of her ski, and somersaulted into the soft snow.
Looks fine. Causal relationship looks good too.D. the last competitor caught the pole with her ski-tip, which made her somersault into the soft snow.
which never refers to an idea or an action. It always is preceded by a noun/noun phrase.E. the last competitor somersaulted into the soft snow when the tip of her ski was caught by the pole.
'caught by the pole' sounds awkward. Causal relationship is wrong. She somersaulted because tip of her ski was caught. She didn't somersault when the tip of her ski was caught.