Phase 1 (3 weeks)

Pour the grain alcohol into a 1/2 gallon jar with a lid.
Add all of the blackberries.
Crush the blackberries with a wooden spoon.
Seal the jar and let it sit for 3 weeks.
Shake the jar every other day.

Phase 2 (2 weeks)
After the alcohol and blackberries have sat for 3 weeks, you'll make a simple syrup to add to the mixture.

Bring water to a boil and add sugar. Stir until the sugar dissolves then let cool to room temperature.
While the simple sugar mixture is cooling, take your alcohol and blackberry mixture and strain out the remaining blackberries.
Return the alcohol mixture into its jar and pour in the simple sugar mixture.
Seal the jar and let sit for 2 weeks or longer.