There is not much to "do" in Shankarpur in the sightseeing sense — the beach, the fishing harbour, and a short trip up the coast to neighbouring Tajpur are the whole offering. That is the point: Shankarpur exists for travellers who want a quieter version of Digha, with the same sea and sand minus the holiday crowds and concrete promenades.
The fishing harbour at the eastern end of the village is the only real spectacle. Several hundred trawlers tie up here between trips and the fish auction at dawn is the busiest thing for kilometres in any direction.