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