There are 2 ways to do this:
1) Co-op. Simply play with a friend/partner and defeat the Rakk Hive, the Vault Boss, Sledge, Krom or Flynt. You only need to kill one of these bosses to unlock the trophy.
2) Solo. Proceed to defeat any of aforementioned bosses by yourself. Once you've done that, DO NOT "turn in" the mission. For example, if you defeat the Vault boss, don't report back to Tannis. Instead, save your game and exit to the main menu. Start a split-screen Co-op game and once the game loads up, the trophy will unlock.
The choice is yours!
Happy Hunting :)