There are 2 ways to do this:
1) Co-op. Simply play with a friend/partner and complete any 15 missions.
2) Solo. Proceed to completing any 15 missions of your liking (bounty board missions work best for this). However, after doing a mission, DO NOT "turn in" the mission. For example, when doing the "Get A Little Blood On The Tires" mission, do not turn in the mission to the Bounty Board after roadkilling 10 enemies. 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 best bet to be completely safe with this method is to accept bounty board missions in one sitting and then "turn in" all at once in split-screen mode. If you choose this route, the trophy will unlock after the 15th mission has been completed on split-screen load up. To be extra safe, turn in the completed missions to the bounty board during split-screen play prior to going back to playing solo, this rinse and repeating.
The choice is yours!
Happy Hunting :)