Easy breezy. While playing with the Acorn, transform yourself into an Oak and start roaming around the mission areas. As soon as you see two or more regular zombies (coneheads, brown coats or TV heads), walk around them until they are side by side and press RB. The Oak will throw a rolling tree at them for instant kill. The achievement will pop when you kill 20 groups of at least 2 zombies.
(i) zombies holding doors and flags protect the others from the tree branches;
(ii) if the branch hits a wall or object on the street, before reaching the zombies, it will be destroyed and no one will be killed by it;
(iii) to kill heroes, shoot them first with your regular gun and use the "roll for damage" as your final blow.