For this hidden trophy you have to kill either a target, guard or a civilian with the Fire Axe for the trophy to pop. This trophy can be earned smoothly within your first playthrough, the Axe can be found and the kill executed without any hiccups all in the same mission i.e Mission 10: Basement Killing. To use the Fire Axe simply equip it and press , it usually takes 1-2 hits for a kill. Note: 47 draws the Axe back before he takes a swipe which takes about 1 or 2 seconds. Just factor this in when trying to kill someone because if you attack too late then it may allow your victim enough time to runaway. Very much like killing with the Knives, in order achieve a clean kill it may be wise to sneak up to someone from behind to avoid any complications.
Getting the trophy in Basement Killing should be no hassle. Set off the Bomb to draw out the fireman then run into the department and take the Axe along with the fireman's disguise. Simply kill your target with the Fire Axe, he is on his own and providing he does not spot you, you should be able to perform a clean kill. For more details on obtaining the Fire Axe and carrying out the kill, see the Professional Mode Guide and read under Basement Killing.