This trophy is for getting the first strike boast at the end of a match three times. This means you had the first kill of another player during the game. Obviously this is heavily dependent on the quality of your opposition. You will know instantly if you have the first kill as you get bonus points for it in the game and you can watch the kill feed in the top right hand corner of the screen. Although you know you have the first kill you need to finish the game and be awarded the boast at the end of the game when the scoreboard is revealed. Likewise, the third time you get the boast the trophy won't pop until the end of the game, the trophy will likely pop before the scoreboard is revealed.
The easiest way I found to get the first kill is be a Pea Shooter during a Gardens and Graveyards game. If you know where the enemy spawn you can start moving there while the countdown timer is going at the beginning of the game and as soon as the timer gets to zero use your hyper mode to cover any remaining distance. You then throw a chilli bean bomb where the players are spawning and try to kill or weaken the spawning players and finish them off with your usual attack. I have gotten three+ kills at the beginning of the round using this attack method.