Open the can of lychees and pour the syrup into a measuring cup. Set the lychees aside in a bowl. Rinse the blackberries and blueberries, then pat them dry so everything is ready to go.
Add the blackberries, 3/4 cup lychee syrup, and lemon juice to your blender. Blend on high until the mixture looks completely smooth and inky purple. This usually takes about a minute.
Set a fine-mesh sieve over a large pitcher. Pour the blended mixture through it in batches. Press the solids with a spatula so you squeeze out every bit of juice, then toss the seeds.
Pour the acai juice and blueberry juice cocktail into the strained mixture. Stir well until the color looks even. Taste it now, because the flavor should be fruity and slightly tart.
Cover the pitcher and place it in the refrigerator for at least two hours. Chilling lets the flavors blend together. It also means your punch will be icy cold when guests arrive.
Drain the lychees and pat them dry with a paper towel. Gently press one large blueberry into the hollow center of each lychee. The blueberry peeks out like a pupil, and you now have creepy eyeballs for your punch bowl.
Pour the chilled berry mixture into your punch bowl or a large pitcher. Add the stuffed lychees so they float on top. Stir in the lemon-lime soda gently so you keep the bubbles.
If the party is for adults, stir in the spiced rum or gin now. Fill glasses with ice. Ladle the punch over the ice and make sure each cup gets a few eyeballs.