There are 5 tools in The Last of Us. Finding all of them is necessary to upgrade your weapons. They are also a requirement for the "For emergencies only" gold trophy. Only finding the toolboxes won't earn you the trophy though. You still got to upgrade every weapon in the game (can be done at workbenches).
The tools have fixed locations and must be picked up in correct order during one playthrough. They do carry over to New Game+. Getting them via chapter select won't help with the upgrades or achievement.