Whisk 2 cups milk and chocolate pudding mix in a bowl. Let stand until slightly set, about 5 minutes. Spread pudding in the bottom of the pie crust. Sprinkle 1/4 cup shredded coconut on top.
Whisk remaining 2 cups milk and coconut pudding mix in a bowl. Let stand until slightly set, about 5 minutes. Carefully spread over the shredded coconut layer. Sprinkle chocolate chips, remaining shredded coconut, and slivered almonds on top.
Refrigerate until chilled through and set, at least 30 minutes.
