This is even more impressive once you know how it was made, which was by the ancient lost wax method. This method has been around South India for at least 1000 years, perhaps much longer. First the statue or object is carved in wax (imagine 20 feet of that) Then the wax is covered firmly in plaster of Paris or a clay, and strong enough to hold the weight of the potential object. After that is all hardened, it is heated just enough to melt all the wax, which is drained, making a hollow mold. The entire thing is turned upside down, and molten metal is poured through the one hole at the top (bottom of the statue). After a few days of cooling, the clay is chipped off, revealing the beautiful statue. For this one, I imagine they built strong scaffolding, or used machinery.
I witnessed a pour of a much smaller custom statue at Swamimalai. That consisted of two strong men with steel bars, and the cauldron of molten metal in a pot out between them. In unison, they turned the cauldron to make the pour. But that was only about a foot in size.
Boss and I were in Swamimalai on our arapadaveedu pilgrimage, and looked up the sthapathi who did the pour for Iraivan temple's lingam (Kauai) base, which was 5 tons. This Nataraja was 8 tons. The base for Kauai's lingam was panchaloka, which is traditional, but this Nataraja had 8 metals instead of 5. The town of Swamimalai is renowned for it's metal sculpturing, and they do custom work.