The DioField Chronicle

This can be done in the Main Quest story mission "The Horace Threat" and therefore cannot be missed. Each Gigas needs to be downed twice to be defeated (there are 2 of them). The achievement should pop after you beat either.

The battle is not too difficult - save your Bahamut ability for the Gigas, and get out of the way or interrupt before they fire their abilities (red marker on the map shows the AoE).