For this hidden trophy you need to kill 18 people with the Golf Club for the trophy will pop. To kill with a Golf Club it must be equipped and just like any other weapon, press to launch an attack. It may take 2-3 clean hits for each kill. The Golf Club is found in the target's bedroom on the 2nd floor of the villa in the Mission 1: Anathema. Like Jack the Ripper you do not have to get the kills all in one go, you can get your 18 kills over the course of the game. For example you can get 3 kills with the club in one mission then 7 in the next, on the strength that you actually complete the mission where the kills were performed only then will they be legit and you will only need 8 more kills for the trophy.
Earning your kills throughout the 20 levels is not really ideal in respect to the time it may take and the restarts which you may be forced into if you die. The most stress free time to get this trophy is when you are on your clean-up playthrough. The best level is Mission 10: Basement Killing. See 47 Kills in a Mission for a guide on how to get the kills.