A gate card is the cards that can be found in battles and will change the weather to your advantage.
Usually the gate cards will appear if you destroy buildings.
There are 6 types you have to get for the achievement and they are:
Pyrus, Aquos, Subterra, Haos, Darkus and Ventus.
Also note that if you for example need the Pyrus Gate card then you have to play with a Pyrus Bakugan, example Neo Dragoniod and the same for the other cards as well.
A easy way to get this achievements is to use a second controller and go to Duel in Battle arena and choose the Bakugan you need for each type of card and wait until that card appears under the battle. (In duel you don't need to destroy buildings for the cards to appear because they appears randomly on the map)
When you have collected each type of Gate card the achievement will unlock.
*Credit goes to Sakura460 from x360a*