To play as the Vampire, and thus unlocking this achievement, you'll need to destroy 20 gravestones in one playthrough.
Gravestones will not appear on every level, but are common. They're appearance is pretty recognizable as there'l be a number of gravestones situated in close proximity.
For every three gravestones you destroy a ghost will appear seeking his vengeance for disturbing his peace. The ghosts will attack you, but are invincible, so you'll need to try and avoid them as much as possible whilst continuing to destroy the rest of the gravestones. When there are four or five ghosts all hunting for your blood, it becomes a little trickier, but they aren't too difficult to avoid.