Upon defeating the boss Havoc Skytank outside of Hope's apartment, a cutscene will trigger and the achievement will pop once you switch over to Sazh and Vanille in Nautilus.
Defeat the hulls and turrets first, and then stagger the last and main component of the boss to deal massive damage. I ran the following Paradigms:
COM/COM/MED
RAV/COM/MED
MED/SEN/SYN
COM/COM/RAV
COM/SEN/SYN
MED/SEN/MED