For emergencies only Trophy in The Last of Us Remastered

You’re introduced to workbenches pretty early in the game. These are dotted throughout each chapter and can be used to upgrade your weapons using parts. Work benches are the only time you will be able to upgrade your weapons. Upgrade parts can be found just pretty much anywhere and everywhere in this game, coming in increments of 1's, 5's, 10's, 25's, and 50's. Salvageable or upgrade parts appear as in the game. You will need a total of 2,510 parts to get all of the upgrades.

As with supplements, to completely max out all your weapons you will need to at least venture into a New Game+, which you should be doing anyway for the New Game+ completion trophies. If you are thorough enough in your exploring and looting, you should be able to wrap this up sometime during the later half of your second playthrough. If not, you will have to go into a third and play until you get enough parts. As a result of this you might want to leave some of the early weapons until last (eg. 9mm, Revolver etc.) so that you don't have to wait till later in the game to get other weapons before finishing them (Thanks diagnonsense for pointing this out).

Keep in mind however that even if you have enough parts to upgrade a weapon, a lot of the upgrades will require various tool kit levels. As you may have noticed in the upgrade menu, some upgrades have a requirement; these are the tool kits required. Although tool kits are somewhat a collectible in the game and must be picked up in order to unlock the next tier of unlocks for you, they appear in locations that are relatively hard to miss. The max tool kit level is 5 but there are more than 5 tool kits to find in case you do miss some. These do carry over to New Game+ so you won’t have to pick them up again.

Here is a list of the different weapons/upgrades and their costs:

-Weapon Holsters (purchasing these is not required for this trophy)
Pistol: 75
Long Gun: 75

-9mm Pistol (Chapter 2)
Reload Speed: 15 > 20 > 25
Fire Rate: 20 > 30 > 40
Clip Capacity: 15 > 20 > 30 > 40

-Revolver (Chapter 3)
Reload Speed: 15 > 20 > 30
Fire Rate: 20 > 30 > 40

-Shorty (Chapter 6)
Reload Speed: 15 > 30
Fire Rate: 30 > 40 > 50
Clip Capacity: 20 > 30 > 40 > 50
Recoil: 20 > 30
Spread: 20 > 30 > 40 > 50

-El Diablo (Chapter 7)
Reload Speed: 15 > 25
Fire Rate: 20 > 30 > 50
Clip Capacity: 30 > 50
Armour Piercing: 75 > 75

-Hunting Rifle (Chapter 3)
Reload Speed: 15 > 30
Clip Capacity: 20 > 40
Scope: 25 > 35
Armour Piercing: 75 > 75
Power: 60

-Shotgun (Chapter 4)
Reload Speed: 20 > 30 > 40
Fire Rate: 15 > 40 > 50
Clip Capacity: 15 > 30 > 40 > 50
Recoil: 20 > 40
Range: 30 > 50

-Bow (Chapter 4)
Reload Speed: 30
Range: 20 > 30 > 50
Draw Speed: 20 > 30 > 50

-Flame Thrower (Chapter 8)
Reload Speed: 20 > 40
Range: 40
Power: 60

Total Parts Required: 2,510 parts

For reference here is a list of tool kit locations if you wish to use it (Credits to Wozamil):

The Last of Us Collectibles Guide & Shiv Doors/Optional Conversations/Joke locations