Place the lime juice in a small pot. Bring to a simmer and cook until juice is reduced to an almost syrupy 2 Tbsp. Remove from the heat and cool to room temperature.
Preheat oven to 350 degrees F. Place the tart shells on a baking sheet. Prick each a few times with a fork (this will prevent puffing when they bake). Bake the tarts 15 minutes. Remove from oven and cool to room temperature.
While that occurs, place the cream cheese, sugar and lime zest in a bowl. Beat with an electric mixer until well combined. Add the egg and reduced lime juice and beat until the mixture is very smooth. Divide and spoon the cream cheese mixture into the tart shells. Bake 20 minutes, or until filling is set. Cool tarts to room temperature, and then refrigerate until ready to serve. When ready to serve, carefully remove the foil liner from each tart and set on a serving tray. Top each tart with berries, dust with icing sugar, and serve.