The Last of Us is a game about scavenging more than it is about finding ready-made weapons and using them.
Throughout the course of the game, you'll have to upgrade your weapons, but the only way to do so is through the use of tools—five of which can be found scattered throughout the game's many levels.
You'll need to acquire these toolboxes in order to make upgrades to your weapons and in doing so, earn yourself the "For Emergencies Only" trophy/achievement once you have everything upgraded to the max.
Each of these tools has a fixed location and must be picked up in the correct order during a single playthrough. Fortunately, they carry over into the New Game Plus mode, so you'll be able to upgrade your weapons from the get-go.
Bear in mind once again that you'll have to pick them up in the right order, in a single playthrough. Using Chapter Select to acquire them will not help with upgrades or serve as progress towards the acquisition of the trophy/achievement.
Kudos to PowerPyx for putting this video guide together.
Timeline:
#1 – Bill's Town (Graveyard) – 0:05
#2 – Pittsburgh (Alone and Forsaken) – 0:30
#3 – The Suburbs (Sewers) – 0:52
#4 – The University (Science Building) – 1:25
#5 – Bus Depot (Highway Exit) – 1:55