Crack the hard shell of the tamarind pods with your hands and remove it from the sticky middle. Peel off the tough veins as well and discard the veins and hard shells.
Fill a medium saucepan with water and bring to a boil. Add the peeled tamarind pods and reduce heat to a simmer. Simmer for 10 minutes then remove from the heat and let steep for at least 2 hours or overnight.
Remove the hard seeds from the soft pods and place the pulp in the blender.
Add the 1 cup of sugar and 8 cups of water to the blender. Blend until the mixture is smooth and the sugar is dissolved.
Pour the mixture through a fine mesh sieve set over a large bowl or liquid measuring cup and use a silicone spatula to scrape the drink through the sieve.
Transfer agua fresca to a large pitcher. Add the 1/4 cup of lime juice and chill until cold.
Serve over ice with a lime wedge garnish.
