To collect a firearm, you must finish a mission while it is in your inventory, or in an ICA box (there is at least one of these in every mission; it will appear on your map). Not every weapon is required, so check the list below before agonizing over a weapon that you don't need. The list is organized according to how soon you are able to retrieve the weapons, and the missions in which each weapon may be found are noted. Agent 47 can carry an infinite number of small weapons, such as pistols, concealed on his person, but unfortunately can only carry one large weapon at a time, such as a sniper rifle, and it cannot be concealed without a glitch.
The weapons required for this achievement are:
SAF SMG - "A Vintage Year"
Snub nose - "A Vintage Year"; "Death on the Mississippi"
TMP - "A Vintage Year"; "Flatline"; "You Better Watch Out..."; "A House of Cards"
Shotgun - "A Vintage Year"; "Death on the Mississippi"; "Till Death Do Us Part"
MP5 - "Curtains Down"; "A Dance with the Devil"; "Amendment XXV"
SLP .40 - Every mission EXCEPT "A Vintage Year", "Death on the Mississippi", and "Till Death Do Us Part"
Bull .480 - "A New Life"; "Death on the Mississippi"
MP7 - "A New Life"; "A Dance with the Devil"; "Requiem"
Air Rifle - "A New Life"
SLP .40.S - "The Murder of Crows"; "A House of Cards"
Desert Eagle - "The Murder of Crows"; "Death on the Mississippi"; "A Dance with the Devil"; "Amendment XXV"
MP9 - "The Murder of Crows"
Kazo TRG - "The Murder of Crows"
SG552 - "The Murder of Crows"
FN2000 - "Death on the Mississippi"; "A Dance with the Devil"
Six Shooter - "Till Death Do Us Part"
Elephant Rifle - "Till Death Do Us Part"
Dragunov - "A Dance with the Devil"
M14 - "Amendment XXV"
You may replay a mission multiple times to retrieve weapons, only be sure to save afterward so the retrieved weapon stays in your hideout. Be aware that the collected weapons do not carry over between playthroughs; they must all be collected in a single playthrough (though you may still use mission select to keep collecting if you've finished the playthrough). Also note that you cannot retrieve weapons from the tutorial mission. Even if you end the mission with weapons in your possession, they will not be retained in the hideout and won't count toward this achievement. To check which weapons you've already collected, select any mission and you'll arrive at a menu to choose which weapons to take with you. Scroll down that list past your custom weapons and the ones you have successfully retrieved will appear. Be mindful that while wearing some disguises Agent 47 can openly carry weapons without arousing suspicion. If all else fails and you are desperate, there is a useful glitch: If you are holding a large weapon (shotgun, sniper rifle, etc.) in your left hand, and your detonator in your right hand, NPCs will not react with alarm or suspicion to the plainly visible weapon, and you may take it where you wish.
For a detailed guide on where exactly to find all the various weapons, click HERE to navigate to a thread on hitmanforum.com describing every weapon in the game. Note that this thread contains information as well on weapons that aren't required for the achievement, so once again, use discretion before putting forth a lot of effort.