Lightly coat one sheet of phyllo dough with cooking spray. Lay second sheet of phyllo dough on first; coat with cooking spray. Lay third sheet of phyllo dough on second; coat with cooking spray. Cut into 12 squares.
Fit squares into each of 12 muffin tins. Repeat with 3 more sheets of phyllo dough, fitting squares over existing squares in muffin tin so cups are formed.
Bake until golden, about 25 minutes. Cool on rack.
While cups are baking, combine cocoa, extract and syrup until smooth; fold in whipped topping. Divide among phyllo cups. Combine berries and top each cup with 1/4 cup of berries.