What is evident from looking closely at the themes that best describe shiva at Elephanta is that they all belong to his "soumya rupa" or his lasya form. Apart from these sculptures (click here for the list of sculptures) Shiva is known to be depicted in two forms - the soumya rupa and the ghora rupa. Most of his stories depict him in one of these two forms.
Now take for example the Nataraja itself, he is said to have performed the dance in both forms. The tandava itself has various parts to it. In all these sculptures Nataraja is said to stand onthe apasmara purusha, hold the damaru, covered in tiger and lion skins and have a snake around his waist.
How did he come around possessing these icons! This leads us back to the story of Bhikshatana Murti. A mythological story that clearly shows how he came to possess these attributes.