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