Blend the amchur, chaat masala, cumin powder, coriander powder, lemon juice, black salt, hot paprika and a little water into a smooth liquid, and chill it.
Boil the potatoes and the mung beans separately. Peel the potatoes and roughly mash them.
Cook the tamarind and sugar together into a sweet-sour chutney, and chill it.
Crack open the top of each puri and fill with the potato, mung beans, chopped coriander, a little chutney and the chilled spiced water.
Sprinkle with chopped coriander and serve immediately.