Place the chopped kiwi, basil leaves, and pineapple juice in a blender. Blend until the mixture is smooth and the basil is fully broken down.
Pour the blended mixture through a fine mesh strainer into a measuring cup to remove any pulp or leaf bits. Set the strained liquid aside.
In a mixing bowl, add the lime gelatin to the boiling water and stir until the gelatin is completely dissolved.
Stir in the strained kiwi-basil-pineapple liquid, the cold water, and the vodka until everything is evenly combined.
Divide the mixture among 8 small shot glasses. Place the glasses in the refrigerator for at least 4 hours until the shots are fully set.