Let egg whites stand at room temperature 30 minutes. Sift flour twice; set aside.
Preheat oven to 350°. Add cream of tartar, almond extract and salt to egg whites; beat on medium speed until soft peaks form. Gradually add sugar, about 2 tablespoons at a time, beating on high until stiff peaks form. Gradually fold in flour, about 1/2 cup at a time.
Gently spoon mixture into an ungreased 10-in. tube pan. Cut through batter with a knife to remove air pockets. Bake on lowest oven rack until lightly browned and entire top appears dry, 40-50 minutes. Immediately invert pan; cool completely, about 1 hour.
In a small saucepan, combine 1/4 cup crushed candies and water. Cook and stir over medium heat until candies are melted and syrupy. In a large bowl, beat cream until stiff peaks form.
Run a knife around side and center tube of pan. Remove cake to a serving platter; cut horizontally into three layers. Place bottom layer on a serving plate; brush with 2 tablespoons mint syrup. Spread with 1/2 cup whipped cream; sprinkle with 1 tablespoon crushed candies. Repeat layers.
Top with third cake layer. Frost top and sides of cake with remaining whipped cream. Top with remaining candies. Store in refrigerator.