To unlock the Vampire, you need to destroy 20 gravestones in a single playthrough. On the map, gravestones are the areas where it is blank on the inside, and have four corners.
Watch out for the Ghosts, who will attack if you destroy two or more gravestones. Ghosts can attack you, but you can’t attack them. The easiest way to evade the ghosts and destroy the tombstones is to constantly run around and break the gravestones until you see the achievment that you have unlocked the Vampire, or you can choose the Jock and charge through the graveyard.
You can also unlock the Vampire by choosing Scientist and using a Giantiser Pill to destroy the graves in a few seconds.