Just reposting this comprehensive and wonderful guide from BlindMango and Lordidude from psnproifles. They did a great job and wish they'd frequent our site as well.
The Last of Us - Multiplayer Missions Guide
A gameplay guide by BlindMango and Lordidude • Published 11th April 2014 • Updated 14th December 2017
A full guide for the "Firefly" and "Hunter" multiplayer trophies in The Last of Us. This includes helpful tips, all of the multiplayer mission objectives and their requirements, along with the exact times the missions occur.
INTRODUCTION TO MULTIPLAYER MISSIONS
For those who want to get very organized and focused, do some pre-planning on the mission objectives for multiplayer, and survive the 12 in-game weeks to get the Firefly and Hunter gold trophies, this is the perfect place. Directly below this text is an introduction describing the basics of multiplayer for new players, if you already know about multiplayer, then scroll down to Mission Objectives.
For Those Just Starting Multiplayer...
The multiplayer for this game consists of fairly standard game modes that function mostly similarly to most other third-person shooter games, though it's a bit more slow paced and stealthy. The difference lies with the "journey" aspect of the game, which is essentially a very basic "mini-game" that takes place in the menus in-between matches. You have a "clan" you have to manage in the menus, and all it requires is that you pick up objects called supplies within regular multiplayer matches and do challenges of your choosing within regular multiplayer matches every now and then, called "missions".
In this game, after you've completed a multiplayer match, the game tells you a "day" has passed and gives you an update on the status of your clan in the menus. So the "journey" the trophies refer to is 12 in-game "weeks" (84 matches) of playing multiplayer.
After a few "days" of playing regular multiplayer matches the game will give you an alert between matches telling you that your clan either has an opportunity to gain 10% more clan members, lose 60% of clan members, or lose 100% of clan members. It then asks you to complete a mission objective of your choosing, but since it's between matches you need to be quick to choose a mission objective. This is why it's a good idea to take a look at the Mission Objectives section below for the exact order and difficulty of each mission objective so you can be ready in advance. The mission alerts you get aren't randomized, so to prepare for when you'll have to choose a mission, definitely see the Mission Times section of the guide. A mission lasts 3 in-game days, so you will have three multiplayer matches to fulfill the requirements.
If you lose all of the members of your clan at some point, you will have to restart your entire 12 week run all over again which will annoyingly push back your progress for the Hunter or Firefly trophies all the way back to the beginning. Avoiding this is very easy though, you will want to save every easy mission objective (which are the green mission objectives in the Mission Objectives section) for -100% risk missions which will wipe your entire clan out if you don't complete the requirement of the mission objective. This being said, +10% population missions and -60% population risk missions may look important, but they are ultimately useless, don't pay attention to those at all - you will want to throw all of the hard and medium difficulty mission objectives at those. -100% risk missions start at week 6, those are the only ones you want to worry about which you'll want to save the easy mission objectives for.
For tips to help you out a lot in multiplayer (including saving yourself if you're failing at meeting a minimum requirement for a -100% population risk mission objective), see Important Tips for Missions below. Best of luck in multiplayer!
Below is a table that displays every multiplayer mission in the order that the game has them in. It is in this order so that you will not have trouble finding them in the relatively short amount of time the game gives you to select a mission.
Explanation of the games "tiered" system:
At the top of the table, the headings are listed as Tier 1, Tier 2, Tier 3, and so on, the "Tier 1" column is the column that will be the minimum requirement to get to pass the mission that you choose, with Tier 2 and Tier 3 simply being stretch goals that will only give you a better advantage for that mission objective, though they are not required.
If you choose that same specific mission objective a second time in your 12 week run, then Tier 1 will NOT be the minimum requirement, Tier 2 will be the minimum requirement, and Tier 3 and Tier 4 will be the stretch goals, and so on. Since this is the case, choose wisely if you want to select a mission objective more than once in a 12 week run!
The colored text in the table is explained below:
Green: Missions are very easy to do and require little to no preparation/prior knowledge.
Yellow: Missions require preparation or perks, or are more difficult/risky to do.
Red: Missions are hard/risky to do and should never be chosen for -100% population risk missions.
Mission Objectives Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Tier 6 Tier 7 Tier 8
Down Enemies 3 6 9 15 20 25 35 45
Executions 2 4 7 12 15 20 30 35
Special Executions 2 4 6 8 10 12 16 20
Revives 2 4 6 8 10 15 20 25
Heal Teammate 5 10 15 20 25 30 35 40
Downs with Molotovs 2 4 6 8 10 12 16 20
Downs with Bombs 2 4 6 8 10 12 16 20
Give Crafting Items 2 4 6 8 10 12 16 20
Mark Enemies 7 14 21 28 35 42 48 56
Downs with Melee 3 6 9 12 15 18 25 30
Shiv Executions 1 2 3 5 7 9 12 15
Downs with 9mm 3 6 9 15 20 25 35 45
Downs with Revolver 3 6 9 15 20 25 35 45
Downs with Shorty 3 6 9 15 20 25 35 45
Downs with Hunting Rifle 3 6 9 15 20 25 35 45
Downs with Semi-Auto 3 6 9 15 20 25 35 45
Downs with Burst Rifle 3 6 9 15 20 25 35 45
Downs with Bow 3 6 9 15 20 25 35 45
Downs with Long-Range 2 4 6 8 10 16 20 24
Downs with Headshots 2 4 6 8 10 12 16 20
As detailed in the tips above, the +10% population missions and the -60% population risk missions are not important AT ALL. You do not need to worry about +10% and -60% risk missions. In fact, at the point that you get to the -60% population risk missions, it may be helpful to have some of your population wiped out to be able to manage them better. Even if there is an entire 60% population wipe, that is no problem at all, as a note, you can still succeed even with one person in your population. It is recommended to read all of the extremely helpful tips above if you have not already.
Important: Use the hard mission objectives for the 60% and 10% population risk missions so that you can keep the easy mission objectives (the green missions in the table above) for the 100% population risk missions.
Below are the exact times that you will encounter these missions:
Week Number First Mission Opportunity of the Week Second Mission Opportunity of the Week
WEEK 1 Day 6: +10% Population Mission -
WEEK 2 Day 4: +10% Population Mission -
WEEK 3 Day 2: -60% Population Risk Mission Day 7: +10% Population Mission
WEEK 4 Day 5: +10% Population Mission -
WEEK 5 Day 3: -60% Population Risk Mission -
WEEK 6 Day 1: -100% Population Risk Mission Day 6: +10% Population Mission
WEEK 7 Day 4: +10% Population Mission -
WEEK 8 Day 2: -100% Population Risk Mission Day 7: +10% Population Mission
WEEK 9 Day 5: +10% Population Mission -
WEEK 10 Day 3: -100% Population Risk Mission -
WEEK 11 Day 1: +10% Population Mission Day 6: -100% Population Risk Mission
WEEK 12 Day 4: -100% Population Risk Mission -
IMPORTANT TIPS FOR MISSIONS
Don't worry at all about any of the other missions at all until you get to the 100% risk missions on week 6, 8, 10, 11, and 12 - the 100% risk missions are the ones you would use the highlighted objectives on the checklist. The missions on the weeks before that that are the ones you SHOULD NOT use the easy mission objectives on. Even the missions that will give you a total of -60% population risk if you don't succeed the mission objectives should not make you worried at all, having 60% of your clan wiped is actually nice because it's less blue cans you have to keep up with and less of a chance of getting sick/hungry clan members after that.
Use the hard objectives (the ones that are red or yellow on the checklist) for the missions that aren't 100% risk missions as you don't need to worry about those missions and you can save the easy objectives for the 100% risk missions.
It's very important to note that if you are not succeeding at your objective during a 100% risk mission, then you can quit out of the game by holding down the PS button on your controller and selecting "Quit Game" DURING a multiplayer match and when you go back into the game you'll notice that the day you were playing did not count and you have another go at your objective!
Having trouble getting anything done in Supply Raid? Then try Survivors, with Survivors you have the possibility of playing up to seven rounds (which is around 20 minutes) and you'll most likely have more focused times to get some of your objectives done. Survivors is also a good game mode to get much more blue cans per round if you're required to get a large number of blue cans per match through your later weeks.