Place tamarind pods, cleaned of all shells and peels, into a saucepan. Pour in 3 cups water, or as needed to cover, and bring to a boil. Reduce heat to medium-low and simmer until water and pulp are reduced by 1/4, 30 to 45 minutes.

Strain tamarind pulp through a fine mesh strainer into another saucepan; discard seeds. Pour remaining 5 cups water through strainer to wash as much pulp as possible into the mixture. If desired, check pulp left in strainer for any hard pieces of peel and shell and add pulp back into tamarind mixture.

Place tamarind mixture over low heat and cook until warm but not boiling, 2 to 3 minutes. Stir sugar into tamarind mixture until sugar has dissolved. If mixture is too thick, add 1/4 cup water. Divide shaved ice into 6 glasses and pour tamarind mixture over shaved ice to serve.