Fallout Shelter

This is going to take some time, but can be shortened immensely by changing your system clock. (Settings > System > Time) Once you reach the +14 time zone, quit the game, turn it back to -12 and reload the game. You do NOT need to reload if you're moving time forward. However, when moving time back without quitting, the game's audio will cut out. Anyway, there's no one solution because every quest is a tad different, but here are some tips to make your questing quicker and smoother:

Obviously first you're going to need an overseer's office. Upgrade this when you have the funds. Faster you get 3 questing teams out, faster you get this finished.

The quests you get at the start of the game should be quite easy. Send whoever you like on them. While doing that, pick out 9 dwellers who you'd like to be your A, B, and C teams. Your job with them will be to send them out in the wasteland to level up and get their special stats as high as possible in the training rooms. (My A team are all level 50 with maxed out special stats.) You can again abuse the system clock to speed up their training times. Certain special stats will really help you out on quests. Agility determines how often your character will shoot. If you notice your dweller getting hit 2 or 3 times before firing back it's because their agility is low. Endurance deals with total health. Higher endurance = less stimpaks needing to be used. Charisma may help with speech checks that pop up on certain missions, but I cannot confirm that.

As your vault gets bigger and gains more dwellers, the quests will start getting harder. You'll start receiving multi-part quests which get increasingly difficult. With that difficulty increase, the loot will also get better. Some quests have up to 15 parts. Other quests require certain weapons or outfits. You'll also notice that the time it takes to reach each location increases with each successive part. This is where moving your clock forward really cuts down on time.

Another "trick" to cut down on time is to equip any animals to your questing dwellers that decrease travel time. I have a cat that decreases return time by 4x. Turns a 4 hour return trip into 1 hour. There are also a few pets (including legendary Dogmeat) that give you an objective multiplier. Dogmeat is x3 objective completion, so if you take him on a mission, it will count as 3 completed. (Thanks Simm)

Always make sure your questing teams have the best weapons. One weapon that really cleans house is the mini-nuke launcher. Not only does it do massive damage to a single target, it also does splash damage to all other targets in the room. Great one to have along on any quest. If you have no legendary weapons, the plasma rifles are probably your best bet. You'll start receiving legendary items from quests once you reach the higher level ones.

Once you have 3 teams out at once, and you're controlling time within settings, the achievement goes much faster. I'd recommend building an extra Hospital and Science Center so that you can have 60+ Stimpaks and Radaways on hand at any given time. That way you can send out your quest teams with max items. That being said, there really weren't a whole lot of quests (even the 15th part) where my team was in real danger of dying. The main issue is when you face irradiated enemies in every single room...the radiation damage really adds up fast. Some missions will have stims/radaway in the plenty. Others will have barely any, so it's better to pack as many as you can when you leave the vault.

One last item. Those little map popups that appear when you have dwellers out in the wasteland...complete those. They count as a completed quest and are often times super short. (Red Rocket is 1 room, Abandoned shack 2 rooms, etc.)

If you have any further questions or have any tips you think I should add, please comment below. Good luck and have fun!

This achievement should take you the most actual play time. You can use the method to move your clock forward to skip the waiting to start and to return. Or if you want to do it all as it's intended prepare to spend a lot of time waiting.

Get you Overseer's Office up to lvl 3 so you can have 3 quests going at once.
Requirements: Space for 2 rooms.
lvl 1 1000 Caps and 18 Dwellers
lvl 2 3500 Caps and 30 Dwellers
lvl 3 15000 Caps and 55 Dwellers

I would also recommend train up all the SPECIAL stats on 3 dwellers or even 9 once you get a bigger vault going. Then trow them out in to the wasteland to level them up. This will take between 2-3 trips off multiple days to reach lvl 50. But this will allow you to plow trough quests like it's nothing. Give them your best weapons, take a few stim packs and rad aways just in case and you should have never trouble finishing a quest or taking a long time.


Then for the quests them self.
If you're are all ready done with:


You can cut down a lot of encounters buy skipping obvious side rooms.

If you have played a couple already you may have noticed that the dwellers tell you if you go in the right direction. Take this with a grain off salt since they are not always right.

I also found that a lot of the time the main objective is on a specific floor in relation to the type off building. I'll try and explain some of them. Keep in mind that sometimes this my not be the case and you end up doing the whole building anyway. But most of the times that I used my guide lines I skipped a lot off rooms.

Vaults


Long Office Buildings


High Office Buildings


For all of these I have notice that the higher quests lvls the objective is always far away. With maybe a few exceptions. But then you normally don't get multiple floors and you just walk in to it earlier then you expected. The lower lvls you sometimes go fast to the top to find the objective on the 3 floor. But that is just my experience.

Save your critical hit for hard enemies and bosses. This way you don't have to deal with reinforcements witch should save you some time and make these encounters a walk in the park. Examples for hard enemies Deathclaws,Radscopions and sometimes Raiders.
Bosses have a red Skull next to there health bar. They can be 3x times as strong so kill them quickly since they can do massive damage and even insta kill your lvl 50 max SPECIAL dwellers if you don't look out.


The final objective is 98/100 in a 2 or 3 sized room. The only two where the final objective was in a 1 sized room. There could be more, maybe but this is the only two I have encountered out of the 100 I have done. And there both related to this series of quests. I have noted them down below.

The search for Jobinson’s Jersey 8/15
Getcha’ Peanuts Here
The search for Jobinson’s Jersey 10/15
There’s No Crying in Baseball

So if you're browsing in a elevator it's worth it to just go in a big room instead off a 1 sized room.

So I hope that this will help somebody and if you have experienced something that I haven't mentioned let me know and I'll add it in.

Happy Hunting