First of all, you unlock the Multiplayer Combat Maps by completing the Quest Cards. Quest Cards are unlocked in order from 1 to 15 every time you collect 400 Merit Badges. These Merit badges can be Bronze, Silver, or Gold Coins.
Below are the Quest Cards that unlock Multiplayer Combat Maps
Quest Card 3: Alpha’s Plane – Multiplayer
Quest Card 4: Canyon, Night – Multiplayer
Quest Card 7: Beta’s Plane – Multiplayer
Quest Card 8: Mountain, Stormy – Multiplayer
Quest Card 11: Gamma’s Plane – Multiplayer
Quest Card 12: Pillars, Night – Multiplayer
Quest Card 14: Muntz’s Plane – Multiplayer
Quest Card 15: Tepui, Dawn – Multiplayer