Here is the full list of all 12 Vertex Dispenser achievements.
Have two Doppelgängers in play at once.
Complete Episode 2.
Exceed seven colours.
Complete Episode 1.
Complete Colour Puzzle.
Collect the Expand Edges ability on Time to Defend (normal difficulty).
Eliminate the Enemy on Mythic Portal (normal difficulty).
Complete Mythic Portal in 1:30 (normal difficulty).
Complete Slaughterhouse without dying (normal difficulty).
Complete Arcane Lore (maximum difficulty).
Have a dozen white vertices.
Beat m hard AIs with n human players, where m>n.