In a blender add the mango, mango nectar (use the lesser amount), sugar (lesser amount), and juice from lime. Do not throw out the used lime.
Blend those ingredients until smooth adding more liquid if necessary, for your blender to process. Taste and sweeten with additional sugar to your liking.
Sprinkle tajin onto a small plate or bowl. Rub the used lime around the rims of two 12-ounce cups, then dip the rim of the cup into the tajin.
Drizzle a couple spoonfuls of chamoy into the bottom of the cup. Pour mango puree into cup and top with more chamoy and tajin. Garnish with tamarind candy stick and serve immediately.