Affordable Rock Removal...
	Infinite Lunch Boxes and Money...
	Time Lapse (Exploit)...
	Various Achievements...

Tap on any building you want to build. Next, you'll need to choose where to place it. Instead of selecting an empty space, eliminate rocks until you have almost no money left. Now go ahead and place the building wherever you like. The rocks should still be gone but you won't have to pay for their removal.

This exploit requires you to start a game with a brand new vault. Place the rooms you start with, and have the Dwellers occupy them. Complete objectives from there, until you are asked to either "Equip 1 Dweller With a Weapon" or "Sell 1 Weapon or Outfit." Instead of completing either of those objectives (by claiming a reward), which will disable the exploit, complete other missions until both of the aforementioned objectives are listed. From there, you should soon see a mission to "Get 50 Water," or to "Get 50 Food," or to "Level Up a Dweller." You can complete any of these three missions repeatedly, as long as you have not first completed "Equip 1 Dweller With a Weapon" or "Sell 1 Weapon or Outfit" already noted. Completing those repeatable missions is an easy way to quickly amass a pile of lunchboxes and coins.

You can change the time on your device to advance the game so that you don't have to wait. You can do so by heading to Settings > General > Date & Time and disabling the Auto option. Note that sometimes this will cause errors when you return to the actual time, so make sure that all rooms are ready to be collected before you restore the settings.

Complete the indicated task to unlock the achievement.

Achievement	How to unlock
A Better Future, Underground	Upgrade 20 Rooms to Level 3.
A Little off the Top	Change the appearance of 10 NPCs in the Barbershop.
A Vault For My Vault	Collect 10,000 Caps.
Armed and Dangerous	Collect 20 Legendary weapons.
Atom Splitter	Merge 3 Power Rooms.
Better Settler	Level up a Dweller from 1 to Level 10.
Big Pharma	Collect 100 Stimpacks and 100 Radaway on Quests.
Blast From The Past	Collect 20 Legendary Dwellers.
Decorator	Collect all Pieces of 4 Themes.
Dine and Dash	Merge 3 Food Rooms.
Enemy of the Wastes	Kill 500 enemies on Quests.
Fashion Statement	Collect 20 Legendary outfits.
Fashionista	Craft 10 Outfits.
Get Off My Lawn	Successfully stop 50 Raider Attacks.
Hard Work is Happy Work	Successfully complete 50 Room Rushes.
Higher and Higher	Level up a Dweller to level 25.
Home Sweet Home	Build 1 of every room type.
Interior Designer	Craft 1 of every room theme.
Legend of the Wastes	Complete 100 Quests.
Mattress Stuffer	Collect 1000 Caps.
More than Handy	Craft an Outfit, a Weapon and a Theme.
Overachieve Much?	Complete 100 objectives.
Overseer	Level up a Dweller to level 50.
Paint 'n Elbow Grease	Collect all Pieces of 1 Theme.
Prepared For The Future	Make 25 babies.
Project Purity	Merge 3 Water Rooms.
Scraptastic	Scrap 500 items.
Smooth Talker	Make 25 Dialogue Choices in Quests.
Survivalist	Complete 60 Quests.
Urban Ranger	Complete 30 Quests.
Vault-Tec Architect	Build 25 rooms.
Vault-Tec Engineer	Build 50 rooms.
Wasteland Wanderer	Complete 10 Quests.
Weaponsmith	Craft 10 Weapons.
You're Fired!	Kill 10 Quest Bosses.