To obtain this achievement you must find and collect all of the firearm weapons within the game. This includes all weapons that are classed as firearms, such as guns and explosives. You do not need to obtain all of the melee weapons for this achievement. You must pick the weapons up and keep them in your inventory and then proceed to finish the mission with the weapons still in your possession, for them to be classed as 'collected'. You will find a list of all weapons and their location in the following weapon specific achievement descriptions, below.
The only set of weapons that do not have their own achievement are the SMG's, so I will list them here as they are required for this achievement.
Heckler & Koch MP5
The H&K MP5 can be found during the mission 'Tracking Hayamoto.' It is carried by the majority of the guards throughout the mission.
The SMG-SD6 can be found during 4 different missions; 'Hidden Valley', 'At The Gates' and 'Shogun Showdown' being carried by ninja's, as well as inside the guard room during the mission 'Shogun Showdown' and during 'Temple City Ambush' being carried by the assassin.
The Uzi can only be found during 1 mission 'Terminal Hospitality' carried by some of the guards near the dock area. You can also find 1 in a hut on the same mission, along with some ammunition.