Heat the oven to 225 degrees F and line two baking sheets with parchment paper. Beat the egg whites and cream of tartar until soft peaks form.
Add 1 cup granulated sugar one tablespoon at a time, beating until the meringue is thick and glossy. Beat in 1 teaspoon vanilla extract.
Spoon eight mounds of meringue onto the prepared sheets. Bake for 75 minutes, turn off the oven, and leave the meringues inside until completely cool.
Cook 2 cups blackberries with 1/3 cup granulated sugar and lemon juice over medium heat for 6 to 8 minutes. Lightly crush the berries, then refrigerate the sauce until cold.
Scoop the firm coconut cream into a chilled bowl, leaving the watery liquid behind. Whip it with the powdered sugar and remaining vanilla extract until fluffy.
Break the cooled meringues into bite-size pieces. Gently fold most of the meringue, blackberry sauce, and remaining fresh blackberries through the whipped coconut cream.
Spoon the Eton mess into chilled glasses, decorate with the reserved meringue and berries, and serve immediately.