Defeating the BSAA translates to killing the BSAA Rookie Agent. This is best done on Steel Beast as the J'avo run and kill faster than the zombies on other maps.
Since a standard match of Siege Mode has two rounds, both teams can work on this during the same match. Have your Human partner(s) choose Helena, since she has grenades in her loadout. While playing as the Human team, throw all three of your grenades at the Rookie to lower his health. The player on the Creature team should now rush towards the Rookie and finish him off. This will count as one defeat over the BSAA.
When the teams switch sides in Round 2, now the other player can kill the Rookie in the same fashion. This method will net both you and your boosting partner about 20 'Defeats' per hour.
You can check your progress by opening the Records in the Main Menu and going to 'Extra Content -> Siege -> BSAA Agents Defeated.'